Eurytion means 'widely honoured', from eurys, 'wide' and tio, 'to esteem', 'honour'. This is a suitable interpretation for the several people who bore the name, including a Centaur (who admittedly led a riot at the wedding of Pirithoüs and Hippodamia), a herdsman of the monster Geryon, and the son of Actor and Demonassa.

If we are not too happy about the Centaur, then we can try another meaning for him, from eu-, 'good' and rhytor, 'drawer', meaning a good archer. However, even here it must be said that there was some doubt as to whether Centaurs actually used bows and arrows, although eastern artists represented them as archers.