The turkish word for hand is "el", and if for example I talked about your hand I would say "Athos77'un eli". Ignoring the "un" suffix there, which I believe is rather modern, the translation of "Athos77eli" as "Athos77s hand" would be correct.

I know for Kocaeli and think also for the others it however comes from smushin two words together, "Forties" or "koca" with the word "il" which means "province". So it's not surprising to see it in the names of provinces. So if I was talking about a province named after you I woud say "Athos77 ili". As in "Athos77s province". The change from "ili" to "eli" happens when the last vowel of the first word is an "a" (Just taking "kocaeli" and possibly "kırklareli" as an example here). In turkish vowels are distinguished between "deep" (aoıu) and "high" (eiöü) and "wide" (aeoö) and "narrow" (ıiuü). The jump from a deep and wide vowel (in this case a) to a high and narrow vowel (i) sounds very jarring in turkish so the high and narrow "i" is changed to a high and wide "e" to make the transition from "a" less jarring as it only breaks one category instead of both at the same time. I hope that made sense.