Hitman was never called that in his own series. He called himself that, in his debut from Bloodlines, but every other time he was Tommy Monaghan.
Ennis also seriously downplayed his X-ray vision powers, until he phased it out completely. Really, the powers were pointless, the way Ennis wrote him.
The mutant eyes did make for a memorable moment when Noonan died, and he couldn't cry any tears for him.