I think it'd be pretty cool if you could rename weapons in the game to whatever you please. I think in the post-apocalyptic world of Fallout, a gun would be more of a friend and a companion rather than just a tool. After all, it's the difference between life and death. We got close to it with the weapon modifications (After all, nothing was better than taking a Brush Gun from your first killed Veteran Ranger, modding it up, and keeping it for sentimental sake.)
So, if you had a specific Hunting Rifle that always seemed to find it's mark, be reliable, and save your ass in situations, you could rename it "The Lifesaver", or if you going for comedy, you could just rename them to fit specific inside jokes and the like.
It would be fun, and immerse you a little more in your character and the Fallout world.