Eurytus was a grandson of Apollo and the son of Melas. He became a king of Dechalia (possibly this was in Thessaly) and was himself the father of Iphitus.

Eurytus was also the name of a giant who was struck down by Dionysus in the battle of the giants against the gods. It was, too, the name of one of the Moliones, a son of Actor and Molione.

We can take our choice here, deriving the name from eu-, 'good' and rheo, 'to flow' (thus 'fair-flowing', like Eurotas), or from eryo, 'to keep guard', so 'holding fast', or even, like the Centaur Eurytion, from eu-, 'good' and rhytor, 'drawer', so 'good archer'.

This last interpretation would certainly suit the grandson of Apollo, who himself was described by Aristophanes as rhytor toxon, 'drawer of bows', in his play Thesmophoriazusae (approximating to 'Women Celebrating the Festival of Demeter the Law-Giver').