I nickname anything that I think I'll use or that feels significant to have. You can see my current team's names in my signature but I've also got Useless the Raticate, Rocky the Onix, Geodudette the Geodude, Moon Pixi the Clefable, Booberella the Jynx and then several "Mr Munchy" variants of Golbats. Nicknaming is fun but it can be hard to be creative!
Some examples...
Also have Bulbasaur, Charmander and Squirtle as "Salad," "Steak" and "Soup," respectively. They're mixed with some names that can be interpreted as vulgar/inappropriate so I'll spare the public the screenshots.
Oh god I love these so much.