Machaon was the son of Asclepius by Epione, and a brother of Podalirius. He married Anticlea. We mentioned machaira, 'knife' for Machaerus, and this interpretation could also be valid for Machaon, since he was traditionally a surgeon while his brother Podalirius was a 'GP' (a 'practitioner'). The father of both brothers was of course a god of healing.
But his name could also mean 'warrior' on the same basis, if we regard the machaira not as a surgeon's knife but as a weapon. And his name still works out as 'warrior' if we derive it from mache, 'battle', 'fight' (compare names ending in this word, such as Andromache). According to some accounts it was he who healed Philoctetes' wound (see Phimachus and also Podalirius).