This is one of those "technically true, but missing the bigger picture" pedantic gotchas.
Yes, Hercules is the Roman name not the Greek name. Yes, barbarian as a term originally meant not-Greek or not-Greek-enough for some Greeks.
But it's not like you're going for full historical accuracy already (or even could if you wanted to). It's just a subjective scale of how accurate do you want to be in what ways that you think are important.
You're not going to speak ancient or koine Greek when playing the game. You're playing game rules that aren't based solely on Greek mythological cosmology. Barbarian isn't a term in DnD for non-Greeks the same way chai tea in English doesn't mean "tea tea," but rather "a spiced Indian tea." Words have multiple meanings. Those meanings can change over time. Those words can have a different meaning in a different language even if adopted from the same source.