I guess one way to translate this would be У древних греков было слово для этого, but I'm wondering if there is a more natural way to express it in Russian. (For example, maybe it sounds better to start with В древнегреческом языке...?)

Incidentally, there was a 1920s Broadway play called "The Greeks Had a Word For It," which became the basis for the 1953 film comedy How To Marry a Millionaire. So in the context of the play, the "It" for which the Greeks had a word was, presumably, gold-digger (slang for "a woman who seeks a wealthy husband") and/or gold-digging.

But "the Greeks had a word for that" is sometimes used jokingly to suggest any kind of sexual perversity, in a wink-wink, nudge-nudge way:
TOM: My girlfriend always wants to let her dog sleep in the bed with us.
BILL: Hmmm, didn't the Greeks have a word for that?
TOM: Shut up, that's not what I meant!