I have a long rifle I named "Jen Ellen" after my wife's best friend and maid of honor in our wedding who passed away suddenly at age 29......It was a common practice in the 18th century....
Mine are pretty easy to name, my 1911's are all called 1911. I am sure every one can see how boring my naming process is. Completely without imagination!
I use to have an M1A Nation Match. I had "Blessed are the peacemakers" engraved just below the hand guard on the left side on the stock. Looked very cool. I called it my Peacemaker.
Not necessarily a name, but when equipped with a bayonet and a 75 round drum I refer to my Yugo underfolder AK as "The Party Pooper", because it certainly would. I mean... Depending on the party, I guess.
...I also put a "Mr. Yuk" fridge magnet on it when in that configuration, just for the lolz.