I nickname every single Pokémon. Even ones I'm breeding that will never be used. Usually it's whatever name comes to mind, unless I'm theme-naming a team. And they're almost always real people names. Actually let me just boot up X and read a few...
Tanni, Jared, Nathan, Jeremy, Helen, Satoshi, Surge, Jimmy, Antoinette, Clara, Dale, Yan, Axel, Ezra are all hanging out in one of my boxes. My main team was Rachel, Amanda, Flynn, Emma, Anthony, and Blaziken (no nickname event torchic ♥♥♥♥♥♥♥♥). My secondary team was Pamela, Harry, Riley, Andy, Larry, and Kinniekins (from Shauna).
So literally. Anything that comes to mind. And I try not to repeat, which leads to uncommon or maybe not actual names but hey. They're all my bbys. And it's fun to know that I have that kind of ridiculous knowledge bank of names in my brain.