Melchiades and Miltiades

Thought the name "Melquíades" was cool and wanted to know the etymology. Every source I've found (which is nothing trustworthy: baby name sites, faith sites, AI) just says it's from Greek "Miltiades." It doesn't help that there was a pope known as both Miltiades and Melchiades.

I don't really buy it. For one, I don't see anything about a /t/ to /k/ sound change, in or between those languages. I think that Hebrew has some role here. My guesses are

I think, if it is Greek in origin, it is still borrowing "Melchi-" ("my king" or "king of") from Hebrew (compare "Melchizedek" and "Melchior").

Perhaps it's even a hellenization of "Melchi" by adding the patronymic suffix "-ades"?

Does that sound right? Any idea where I could find a source to support or refute those ideas?

https://redd.it/1wnscv5
@r_etymology