Since these names would have first been introduced before the liturgical/spoken languages diverged (and not from later localized figures like saints), language-specific versions of names developed through the same process by which, say, Latin evolved into the Romance languages. At a given point in Late Antiquity, three Latin-speaking Christians in (what are now) France, Spain, and Italy could all be named Iohannes, since that was just the Latin form of the name that they could have read in the Bible/heard at Mass. As time went on, and their descendants continued to use the name (while at the same time they're "continuing" to use the language that used to be Latin) each version of the name would get further and further from the "original" Iohannes until we end up with forms as different as Jean, Juan, and Giovanni.

I imagine the case in Byzantium is quite similar, or even more so since there weren't numerous "child" languages as Latin had in Old French, Provençal, Italian, etc. - though I don't know enough about medieval demotic Greek to say if there were any changes beyond "they started pronouncing vowels funny." Ioannes (Ἰωάννης) is always Ioannes (in writing, at least).