In fallout 3 or New Vegas? In Fallout 3 it is, if you speak to Pinkerton. Fallout New Vegas, however, does not allow you to yet, though it looks like it may be possible to in Old World Blues.
You can change your hairstyle if you join the Kings in NV, and from your robot butler and a few other characters in Fallout 3. If you get plastic surgery from Pinkerton and you look completely different, everyone somehow still knows it's you.