I usually name my favorites, not necessarily the ones I shoot the most, just the ones I really like and have some character. For instance, I have a Winchester model 67 I call Grandpa. My Saiga is Natasha, the Russian Sledgehammer. A favorite Finn M39 is Kaarin, the Finnish version of Karen which also happens to The Boss's name.
I name absolutely everything. A piece of gum I see on the sidewalk? Yep, I name it. Floaters in the toilet? Named. My guns? Each has at least a first name, middle name, nickname, and last name. None have the same last name as I don't want it to be weird if they reproduce in the loaded pile that lays on the kitchen floor.
I've only named one. My 6" GP100 is named Maggie. I've tried naming others, but couldn't come up with anything good. Still pondering though. I call them all my "kids" anyway.
I have given a couple guns names due to the sentimental value in them like my weapons that have been given to me by my parents. For instance, I have a .410 gauge Mossberg that was my first gun that I call Heritage
I build custom flintlock long rifles and I have named the ones that I built for myself. This was a common enough practice in the 18th century that historical references can be found fairly easily.
I have a .45 caliber J.P. Beck style rifle named "Amanda", a .62cal/20 gauge smoothbore fowler named "Gwenalene", a .50 caliber Jacob Dickert rifle named "Liberty" and a .36 caliber Isaac Haines rifle named "Abigail"