I think it's fine. It doesn't sound pretentious like most surname names do (
Chase,
Maddox), and doesn't sound doggy-eager like most occupational surname names do (
Cooper,
Sawyer). To me it sounds sort of rustic, and makes me think of a person who is at least not overfed.
The thing I don't like is that the T tends to get dropped. People don't say Hun-Ter. They say Hun'er. It comes off sounding sorta slick. IMO. I don't think Hunt makes a good name at all. But if
Hunter were a name I wanted to use, I couldn't care less if animal rights softies were bothered by the mere idea of people hunting. Animals are hunters too, ffs.