Ulysses (or Ulixes) was of course the Roman name of the great Odysseus, king of Ithaca. The names are sufficiently different for us to look for a separate origin for Ulysses. Robert Graves suggests one in Greek oulos, 'wound' and ischea, 'thigh', referring to the boar-tusk wound in his thigh that Odysseus received when he went out hunting on Mount Parnassus as a boy with the sons of Autolycus.
This wound stayed with him all his life, and it was because of it that Euryclea, his old nurse, recognised him when he eventually returned to Ithaca from Troy. On the other hand, if the Latin form of the name did gradually evolve from the Greek, it must have been through an Attic variant such as 'Olysseus'.