Nicely found. However, the monogram
can also be solved Michaeliou, with no need for the 'monachou', as the N is possible but not necessary for the solution (it is formed out of M and X). It's a much rarer name than Michael, but still
known for a small number of persons. The DO comment, I see, mentions this solution, but the argument for their preferred reading does not make sense - I quote: "but it seems more likely that we would find the somewhat common name Michael in conjunction with the somewhat common title of monk". This only applies when we have to chose between Michaelios monk and Michael monk. Then indeed, the latter solution must be preferred.
Can you find an example where there's a higher degree of certainty?