Books, chapters and lines in the Etymologies:

Namesakes are numbered for identifications purposes as is praxis in the Greek Mythology Link. If a name is not linked, see the Dictionary for further details.

Excerpts from Isidore's Etymologies are in red.

Sources
Abbreviations

Achaeus: 9.2.72.

"The Achaians, also known as Achivians, were named after Achaeus, son of Jupiter."
The eponym of the Achaeans, Achaeus ₁, is otherwise known as son of Xuthus ₁ & Creusa ₁ [Apd.1.7.3; Pau.7.1.6; Strab.8.7.1]. Achaeus ₂, son of Poseidon & Larisa ₁ is also regarded as eponym of the Achaeans [DH.1.17.3].

Agenor: 14.4.1.

"Europa was the daughter of Agenor, king of Libya, whom Jupiter carried to Crete after she had been abducted from Africa ... This Agenor is the son of Libya, after whom Libya, that is Africa, is said to have been named ..."
Usually, Europa is believed to have been abducted in Phoenicia where she was born [Apd.3.1.1]. Apollodorus says that Agenor ₁ was born in Egypt but departed to Phoenicia where he reigned [2.1.4]. Apollodorus calls him son of Poseidon and Libya [3.1.1] whereas Nonnos calls him son of Belus ₁ and Anchinoe [3.297]. Hyginus calls Agenor ₁ "a Sidonian", and says that Phoenix ₁, brother of Europa, set out for Africa, looking for her [Fabulae 178]. Ovid calls Europa "the Tyrian maid" [Fasti 5.605].

Amphictyon: 13.22.4.

"The third flood was in Thessaly in the time of Moses and Amphictyon, who was the third to reign after Cecrops."
The Athenian kings are reported to have reigned in this order: Actaeus ₁, Cecrops ₁, Cranaus, Amphictyon ... Actaeus ₁ was the first king of Attica, Cecrops ₁ received the kingdom from him, and when Cecrops ₁ died, Cranaus came to the throne, being later expelled by Amphictyon [Pau.1.2.6], who is called son of Deucalion ₁ or regarded as AUTOCHTHONOUS [Apd.1.7.2, 3.14.6].

Andromeda: 15.1.19.

"The Palestinians built the seaside city Joppe of Palestine. There a rock is displayed which still retains traces of the fetters of Andromeda."
Andromeda is usually known as an Ethiopian princess. Yet Western and Eastern Ethiopians must be distinguished. The Ethiopian Memnon, who fought in the Trojan War, came from the East, and was son of Tithonus ₁, the founder of Susa [Strab.15.3.2].

Apis: 7.11.85, 9.2.72.

"Serapis is the greatest of all the Egyptian gods. He is that Apis, king of the Argives, who travelled to Egypt by ship ... Among the Egyptians Apis was the bull dedicated to Serapis."
"After Apis, the king of the Greeks, died, his son Argos succeeded to the kingship ..."
The sacred ox worshipped by the Egyptians (Apis ₁) appeared to Telethusa in her dreams [Ov.Met.9.691]. The stern tyrant Apis ₂, who called the Peloponnesus Apia after himself, was conspired against and slain in Hellas either by Thelxion and Telchis, or by Aetolus ₂ [Apd.1.7.6, 2.1.1]. According to Apollodorus he left no child and was at his death regarded as a god (Sarapis, = Serapis), being avenged by Argus ₁, "the all-seeing", who is not the son of Apis.

Attis (Atthis): 14.4.10.

"There was a certain Granus, a native of Greece, after whose daughter's name, Attis, Attica was named."
These names are usually rendered as "Atthis" and "Cranaus" [Pau.1.2.6; Apd.3.14.5-6]. Otherwise, Attis is the young Lydian dear to Cybele who went mad and castrated himself, turning into a pine tree after death [Pau.7.17.9-11; Ov.Met.10.104; Ov.Fast.4.223; Nonn.25.311].

Belus: 15.10.9.

This is Belus ₂, mentioned by Ov.Met.4.213; Nonn.18.229; Vir.Aen.1.620, 1.346, and Lib.Met.34.

Cadmus: 1.3.6:

"Cadmus, son of Agenor, first brought seventeen Greek letters from Phoenicia into Greece: alpha, beta, gamma, delta, epsilon, zeta, iota, kappa, lambda, mu, nu, omicron, pi, rho, sigma, tau, phi. Palamedes added three more to this at the time of the Trojan War: eta, chi, omega. After him the lyricist Simonides added three others (psi, xi, theta)."
The mythographer Hyginus says, by way of introduction, that the MOERAE invented seven Greek letters (of which only six are visible in his text): alpha, beta, eta, tau, iota, and upsilon. Then he refers to other sources which claim that Mercury (Hermes) conceived the letters by observing the flight of cranes which form letters when they fly. Then says Hyginus that Palamedes invented eleven letters, Simonides four (omega, epsilon, zeta, and phi), and Epicharmus of Sicily two (pi, and psi). He says further that Cadmus took the letters which he introduced in Hellas from Egypt, where Hermes had brought them [Fabulae 277].

Callisto: 3.71.35.

"So it was with Callisto, daughter of King Lycaon ..."
So Pseudo-Eratosthenes, Catast. frag. 1, and Callimachus [Hymn to Zeus 40]. Apollodorus gives several accounts concerning her father: either Nycteus ₁, or Lycaon ₂, or Ceteus ₁ [3.8.1-2].

Cronos: 8.11.31.

"... the Greeks say he has the name Cronos, that is, "time", because he is said to have devoured his sons: that is, he rolls back into himself the years that time has brought forth ..."
The identification between Chronos and Cronos is also found in Cicero [De Natura Deorum 2.74]. Other late works kept the difference between the two, for example Nonnos [Dionysiaca 12.15], and the Argonautica Orphica 12, where Chronos appears as father of the HORAE, Aether, and Eros.

Daedalus: 19.19.9.

"Perdix ...copied the spine of a fish, sharping a strip of iron and arming it with the biting power of teeth ..."
Thus he invented the saw. And Daedalus "his mother's brother" and instructor was driven "green with envy, and he threw the boy headlong from the citadel", whereupon Daedalus escaped to Crete as an exile.

Perdix is mentioned by Apollodorus 3.15.8, Hyginus in his Fabulae 39 and 244. Also Ovid narrates the story in Metamorphoses 8.236ff. Hyginus calls Perdix the inventor of the saw, and says hat Daedalus threw him down from a roof. According to Ovid, Perdix was turned into a partridge by Athena when Daedalus threw him down from a citadel. Apollodorus says that he whom Daedalus threw down from the acropolis was Talos ₂ "son of his sister Perdix" herself daughter of Eupalamus, son of Metion ₁ or of Erechtheus. Pausanias 1.21.4 calls him Calos confirming that the boy was Daedalus' nephew.
Isidore says that Daedalus escaped from Crete, "using wings", and "came to Cilicia". The destination of Daedalus is usually said to be Sicily, in the court of King Cocalus [Apd.Ep.1.14-15; Pau.7.4.5-6, 1.21.4; Hyg.Fab.40; Dio.4.79.2] where Minos ₂, looking for him, perished.
Isidore says that Daedalus was the first to make a table and a chair [20.1.1]

Dares the Phrygian: 1.42.1.

"Dares the Phrygian was first to publish a history, on the Greeks and Trojans, which they say he wrote on palm leaves. After Dares, Herodotus is held as the first to write history in Greece."
See the introductory note at Dares' Account of the Destruction of Troy.

Perseus/Persia: 15.1.8.
Medus/Media: 15.1.7, 9.2.46-47.

"Perseus, son of Adea, founded the city Persepolis, capital of the realm of Persia ..."
"King Perseus ... crossed into Asia from Greece and there dominated the barbarian nations."
Apollodorus reports that the kings of Persia descend from Perses ₂, son of Perseus ₁ and Andromeda [2.4.4-5]. Here are other eastern connections of these names:
The Titan Perses ₁ (son of Crius ₁ and Eurybia ₁) fathered Hecate by Asteria ₁ [Hes.The.409-411]. He is called Persaeus in the Homeric Hymn to Demeter 2.24. According to Diodorus, the Colchian king Aeetes consorted with Hecate, and had children by her: Circe, Medea and Apsyrtus [4.45.3]. Diodorus asserts that Hecate was daughter of Perses ₃, himself son of Helius and Perseis (one of the OCEANIDS), and brother of Aeetes.

Otherwise, a daughter of Telemachus and Polycaste ₂ is called Persepolis [Hes.CWE.12]. Nestor had a son called Perseus ₂ [Apd.1.9.9; Hom.Od.3.452], brother of Polycaste ₂.

"Medus, son of Aegius, built Media, and from it his country of Media took its name."
Aegius is Aegeus ₁. Apollodorus 1.9.28, Hyginus (Fabulae 26) and others say approximately the same. The mother of Medus is Medea. Hesiod,, however, says that Medus was son of Jason and Medea [Theogony 1001]. "A king of renown" has also been mentioned as Medus' father [Dio.4.55.7; Strab.11.13.10], but as such may be regarded Aegeus ₁. Medus died fighting against the Indians [Apd.1.9.28]. Hesiod and Pausanias 2.3.9 call him Medeus. Pausanias adds that Hellanicus called him Polyxenus, and that Medea "coming to the land then called Aria ... caused its inhabitants to be named after her Medes." [2.3.8.]

Isidore calls Medus "son of Medea", "stepson of Jason", and "king of the Athenians" [9.2.46]. After the death of Jason, "brother of King Peliacus", Medus conquered the East, founded the city Media, and named the Medes after himself. Peliacus is not Pelias ₁, since Isidore says that "Pelias' children" drove Jason and Medea from Thessaly.

Dorus: 9.2.80.

"Dorus was the son of Neptune and Ellepsis, whence the Dorians take their origin and their name."
Dorus ₁ is the eponym of the Dorians, and his mother is called Orseis [Apd.1.7.23]. Dorus ₁'s father is usually Hellen ₁, the eponym of the Hellenes [e.g. op. cit., Dio.4.60.2; Hes.CWE.4, etc.].

Eridanus: 13.21.26.

"The Greeks also give it [the river Padus = Po] the cognomen Eridanus, from Eridanus the son of the Sun, whom people call Phaeton."
People indeed call him Phaeton (Phaethon ₃), son of Helius (Sun) and Clymene ₁, or of Clymenus ₅ and Merope ₄ [Hyg.Fab.154]. Usually, Eridanus is the name of a river god [e.gr. Hes.The.338], and therefore more ancient than Phaethon ₃. Eridanus is the name of the Po, or the Nile, or the Ocean, or of a fabulous river [Dio.5.23.3]. In it fell Phaethon ₃, having failed in his cosmic adventure [Ov.Met.2.304ff.; Nonn.38.410].

Graecus/Greece: 14.4.7.
Hellas: 14.4.10.
Boeotia: 14.4.11.
Thessalus/Thessaly: 14.4.12.
Lapiths/Centaurs: 14.4.12.
Macedonia/Macedo: 14.4.13.

"Greece is so called from King Graecus, who settled this entire region as a kingdom."
Graecus appears in Hes.CWE.2, that is, Ioannes Lydus, a Byzantine antiquarian (ca. 490-570 AD), who attributes it to Hesiod. Both Graecus and Latinus ₃ (after whom the Latins are called) are sons of Zeus and Pandora ₂, daughter of Deucalion ₁.

A little later (14.4.10), Isidore says that Hellas "is the same territory as Attica".
An unorthodox view; see Hellenes.

"Cadmus ... followed the tracks of a cow ... and took a liking to the place where it had lain down, and so he named the place Boeotia, after the word 'cow' (bos)."
Other authors affirm that the Boeotians were called after Boeotus, son of Itonus ₁ & Arne [Pau.9.1.1.], or of Poseidon & Arne [Hyg.Fab.186], or of Poseidon & Antiope ₅ [Hyg.Fab.157]. Boeotus had a son Itonus ₂ [Dio.4.67.7].

"Thessaly takes its name from King Thessalus."
This Thessalus should be Thessalus ₃, son of Haemon ₇, after whom Thessaly was previously called Haemonia [Strab.9.5.23.]. Thessalus ₂, son of Jason & Medea, was said to have escaped being murdered by his mother. Having been reared as a youth in Corinth, he later moved to Iolcus, where he seized the throne [Dio.4.53.1, 4.55.2]. Thessalus ₁ was son of Heracles ₁ [Hom.Il.670ff.; Strab.9.5.23; Hyg.Fab.97].

"The Lapiths ... were also called Centaurs."
This is yet an unorthodox view; see CENTAURS and LAPITHS.

"Macedonia was called ... afterwards Macedo, who was the maternal grandson of Deucalion."
Macedon is named in Hes.CWE.3, the source of which appears to be Costantinus Porphyrogenitus (Constantine VII, 905-959 AD), who attributes the story to Hesiod. Macedon's mother was Thyia ₂, daughter of Deucalion ₁.

Helle: 13.16.8.

"Phrixus ... fleeing with his sister Helle ... embarked on a ship bearing the sign of the ram ... But his sister, a victim of shipwreck, died in the sea ..."
The usual account is that they were borne through the sky by the Ram with the Golden Fleece. Phrixus ₁ came to Colchis but Helle fell into the sea which was named Hellespont after her [Apd.1.9.1; Hyg.Fab.3; Ov.Fast.3.857ff.; Stat.Achil.1.24, etc.]. Without ram, no Golden Fleece, and without it no ARGONAUTS. Phrixus ₁ gave the fleece to Aeetes [e.g. Apd.1.9.1]. Hyginus says that the ram is the offspring of Poseidon & Theophane, daughter of Bisaltes [Fabulae 3, 188].

Ilus: 15.1.38.

"Ilus, son of Apollo, founded Ilium in Phrygia."
The founder of Ilium, Ilus ₂, is otherwise regarded as son of Tros ₁ [Apd.3.12.2].

Isis/Io: 1.3.5, 13.16.7, 9.2.77.
Epaphus/Libya: 14.5.1.

"Queen Isis, daughter of Inachus, devised the Egyptian letters when she came from Greece into Egypt."
Isis is usually identified with Io, daughter of Inachus. She was loved by Zeus and turned into a cow before she arrived to Egypt where her son, Epaphus ₁, became king. But Isidore knows another Io: "Thus Io was the king of Greece, whence the Athenians are also known as Ionians."
Perhaps Ion ₁ is meant, since Isidore also writes (9.2.77):
"Ion was a powerful man, and he called those same Athenians 'Ionians,' from his own name."
On Libya and Epaphus writes Isidore:
"Libya [i.e. Africa] is so called because the Libs, the African wind, blows from there. Others say that Epaphus had a daughter named Libya with his wife Cassiopeia, and Libya afterwards established a kingdom in Africa."
According to Apollodorus, Libya (Africa) was called after the daughter of Epaphus ₁ & Memphis ₂ [2.1.4], but Higynus says that Libya was daughter of Epaphus ₁ & Cassiopea ₄ [Fabulae 149].

Lacedaemon: 15.1.47.

"Lacedaemonia was founded by Lacedaemon, son of Semela."
Usually, Lacedaemon is called son of Zeus & Taygete [Nonn.32.65; Ov.Fast.4.174; Hyg.Ast.2.21], and Semele is known as mother of Dionysus ₂. Taygete is one of the PLEIADES.

Liparus: 14.6.36-37.

"The Aeolian islands of Sicily are named after Aeolus, son of Hippotes ... Nine of these islands have proper names. A certain Liparus called the first of these Lipare. He ruled Lipare before Aeolus."
Diodorus says that Liparus, son of Auson (a king in Italy), was chased from Italy and came to the Aeolian islands. Later, being helped by Aeolus ₂, he returned to Italy where he died in great esteem [5.7.5].

Lydus/Tyrrhenus: 14.3.43.

"Lydia is an old seat of kingdoms ...Because of its smallness it could not support the two brothers, Lydus and Tyrrhenus, as kings. They therefore drew lots and it fell to Tyrrhenus to leave, with a large number of people, and occupy an area in Gaul that he named Tyrrhenia. Lydia, however is named after Lydus ..."
So also Herodotus [1.7, 1.94ff., 7.74]. Pausanias calls him Tyrsenus [2.21.3]. These brothers were sons of Heracles ₁ & Omphale [Pausanias], or of Atys ₃ and Callithea, or of Telephus [DH.1.27.2, 1.28.1; Hdt.1.94; Strab.5.2.2-4; Hyg.Fab.162].

Manto/Mantua: 15.1.59.
Marsyas/Marsians: 9.2.88.

"They say that Manto, the daughter of Tiresias, brought to Italy after the destruction of the Thebans, founded Mantua."
"The Marsian nation of Italy is so called from Marsyas ..."

Memnon: 12.7.30.

"Memnonides are Egyptian birds named after the place where Memnon perished. They are said to fly in flocks from Egypt to Troy near the tomb of Memnon."
So Pausanias describing a picture: "... and on the cloak of Memnon are embroidered birds. Their name is Memnonides, and the people of the Hellespont say that on stated days every year they go to the grave of Memnon, and sweep all that part of the tomb that is bare of trees or grass, and sprinkle it with the water of the Aesepus from their wet wings." [10.31.6.]
Quintus Smyrnaeus narrates how the Ethiopian soldiers who Memnon had led during the Trojan War were changed into birds by Eos when she saw them lamenting Memnon's death [2.640].

Myrtilus: 13.16.8.

"Now the Myrtoan sea is named from the drowning of Myrtilus, because at this spot he was thrown in by Oenomaus."
The usual account is that Myrtilus was thrown into the sea by Pelops ₁. Myrtilus, charioteer of Oenomaus ₁, caused his master's death by sabotaging the chariot, in order to favour Pelops ₁, who thus got a stolen victory. It is told that later Myrtilus attempted to rape Pelops ₁'s bride and was then killed for that reason [Apd.Ep.2.6-8, Pau.8.14.10, Nonn.20.160, Hyg.Fab.84, 224].

Sardus: 14.6.39

"Sardus, son of Hercules, occupied Sardinia after he came from Libya with a great host, and named the island after himself."
Pausanias mentions the Libyan Sardus as the first who sailed to Sardinia [10.16.5]. According to him, Sardus' father was Maceris, celebrated for his journey to Delphi [Pau.10.13.8, 10.17.2].

The Dice: 18.60:

"Dicing ... was invented by the Greeks during lulls of the Trojan War by a certain soldier named Alea ..."
Pausanias credits Palamedes for this invention [2.20.3, 31.1.1].

Death of Hercules: 9.2.120

"After Hercules perished in Spain ..."
Heracles ₁ (Hercules) is generally believed to have died in Trachinian territory (between Thessaly and Aetolia). He himself constructed a pyre on Mount Oeta and gave orders to kindle it [Apd.2.7.7ff.; Soph.Tra.749ff.; QS.5.645].