The name Ax is a boy's name . Ax and is often added to lists like Nicknames for Boys and discussed in our forums with posts like "Boys Makeover- Two Middles".
From the experts:
Ax makes a somewhat threatening short form of the popular Axel, given to more than 3000 baby boys last year. It can also be used on its own, though it usually isn't. There were, however, seven baby boys named Axe in the US in 2015.