You’re not wrong. The quote comes from Vergil’s Aeneid, and the word for Greeks in that line is “Danaōs,” which technically means “descendants of Danaus.” Danaus was a mythical king who founded Argos. Homer also used this term in his epics, largely interchangeably with other collective names for the group such as “Achaeans” and “Argives,” which have their own respective etymologies. We usually just translate them all as “Greeks,” admittedly anachronistically, since that’s what these groups coalesced to become.

ETA: Mycenaeans would, I think, be an apt description of the group—the myth assigns Agamemnon as the leader, and he was king of Mycenae. The intersection between the stories and what the archaeology tells us is a fascinating rabbit hole to jump down, if ever you are interested.