I stuck with a single PSG-1 sniper rifle for quite some time in Left 4 Dead 2. I named it "BR34K H34DS". On a separate playthrough, I discovered an auto shotgun lying by a blood-stained corpse; she had clearly fought to the death. In her memory, I picked up her shotgun and named it the "Grim Fucking Reaper". It seemed appropriate.
Also, I name every single FY-71 (or as I prefer to call it, "Space AK") I pick up in Crysis, seeing as I tend to hold on to them for hours on end. My most recent one was "Geromy" and he was indeed my best friend.
EDIT: Fun trivia fact! According to Wikipedia, the first two tommy gun prototypes were named the "Annihilator" and the "Persuader".