Aesop = a variant of an epithet of Greek origin, "aithiops" which in turn means "burned", or "of a burnt visage" (see the word origin for Ethiopian). Aesop was of African origin and so the name is actually a descriptor of his physical appearance, not his real name.
I don't think there's anything in particular wrong with this name. It looks good, it sounds good, but... it's probably just too archaic now. It just wouldn't translate well in modern day.
The name AESOP is almost certainly derived from Ancient Greek "Aithiops" meaning ‘burnt-face' (aithein = burn + ops = face), although it was later taken to mean "dark-skinned".