To Revolver, masks were power. The power to do as he wished.
Identity was a weakness. If people knew you, understood you, then they could destroy you. They'd know all your vulnerabilities. Your dueling strategies could be countered, psychological attacks could be organized, and you could be tracked down and arrested. And that would be the end of it.
Which is why Revolver had foregone identity. Now he was simply Revolver, not a true name at all, but instead the description of a consequence. If anyone got in Revolver's way, they'd wish they had a bullet in their head by the time he was done with them.
As long as he wore a mask, he could exert his will however he liked. No more restrictions, he could act according to his own desires. In a way, it was when he took his mask off that he was truly not himself, forced to conform to the rules and expectations of others.
So he continued to wear a mask. As long as he was free, free to crush whomever he so desired, then in time his noble goal would be realized.