Out of some of the Greek characters you don't know, why is Chiron one of them?
He's not just the teacher of Achilles, but practically just about most every big Greek Hero including Ajax, Perseus, Theseus, Jason, Achilles' father Peleus(Chiron was the reason how Peleus met his wife to father Achilles), his best friend Patroclus, the Trojan Hero Aeneas, the God of Medicine Asclepius, and even Heracles(who is also the one who accidently killed him in most myths).
There are more, but they are obscure compared to the ones mentioned above. Not to mention out of the couple Centaurs who weren't a ****, Chiron is the most famous one.