Polymede or Alcimede. He was reared by Chiron, who also named him, giving him a name that referred to the skill in medicine that he had taught him on Mount Pelion.
His name thus means 'healer', from iaomai, Ionic iesomai, 'to heal' - although this attribute has come to be quite overshadowed by his great exploit to recover the Golden Fleece. But perhaps the 'healing' was more moral than physical. One point we must not overlook is that if Chiron named Jason when instructing him as a boy, he must have had an earlier name. He did, and this was Diomedes (which see, although the name is that of quite a different person).
Curiously, Jason's name became very popular as a modern boy's name in the mid-twentieth century, although the inspiration for it is almost certainly not the hero of Thessaly but a modern folk hero such as a film or television actor so named, or even a cartoon character. Even so, the heroic image is still there.