The majority of my Pokemon nicknames are references to things I like, the rest are names I like, or names that the Pokemon or its name makes me think of.
Lately I've been catching so many Pokemon via wormholes that I haven't nicknamed them. Time for that later. I think thoroughly about nicknames, names are important to me.
I just beat the Elite Four (Ultra Sun) this morning with the following team:
Sander (Palossand; because sand)
Buzzwole (still unnamed, my first ultra beast unless you count Poipole),
ZzZzZzZz (Latias, I got her in a trade, I would personally not have named her that)
Ali-Cata (Incineroar; named after a misunderstanding: As a kid I had a comic. Its title was written in a strange font so I misread it and thought it said "Ali-Catas Skrekk" which sounded so exciting and dark, while it really said "Ali - gatas skrekk". I still think Ali-Cata is a great name, and even more so for a cat Pokemon)
Chakka (Leafeon, named after the pet wolf of Beverly Gravlin, whose book I'm still currently reading)
Nebby (Solgaleo; I didn't have the heart to name him anything else, although I kinda think I might do so eventually - I really wanna name him Sanasol, or Solaire)
It was a good team, but it was heartbreaking that I couldn't find space for Lycanroc in that important battle. Nikai was with me since Ha'Ouli City, and would have been extremely useful in the battle against Kahili. I must find a spot for him in the rematch.