Ixion was a king of Thessaly, the son of Antion (perhaps) who married Dia, the daughter of Eioneus. We can interpret his name in a number of ways to suit different incidents in his life. He summoned Eioneus to come to him, saying that he would pay him a handsome sum for the hand of his daughter; instead, he treacherously murdered him.
So perhaps his name comes from hico, 'to come' 'arrive', 'reach' (referring to the fate that came to Eioneus). Later, after attempting to seduce Hera, he was sentenced by Zeus (Hera's consort) to be tied to an endlessly revolving wheel. Here we have a possibility in axon, 'wheel' (relating to English 'axle').
Robert Graves, somewhat predictably, links his name with ixos, 'mistletoe' (see Ischys), saying that the name itself derives from ischys, 'strength' and io, 'moon' (see Io). Perhaps we can decide in favour of a compromise such as 'strong man', accepting that the base of his name is is or ischys, 'strength'.