The name Auriga simply means "charioteer" in Latin. The most popular interpretation is that the chariot driver is Erichthonius, a legendary Athenian king and son of Hephaestus, the god of fire and metalworking, according to Ian Ridpath's Star Tales, which chronicles the stories behind constellations.
Erichthonius was rejected by his father but raised by the goddess Athena, patron deity of Athens, who taught him how to tame horses. He then became the first person to harness four horses in a chariot, potentially explaining Auriga's name.