I never nicknamed mine until I played Pokémon Moon, where I decided to do so with the members of my team. Glad I did, honestly, it was so much fun and really felt like my Pokémon were more... alive, in a way. I'm definitely doing that again! ^w^
I’ve played every edition to the main games of the franchise since I was a kid, and no matter what I’ve always nicknamed my Pokémon. To me, leaving their name alone was like calling a dog “Dog” or a cat “cat”, so it just felt right not just calling them by their species name.
I have Moon too. Personally, I give a nickname to the ones I choose for the main team, to the legendaries and the ones I wish to train hard. Usually I choose names with some connections between the Pokemon and the books I read, but some times I use random names (for example, I named my Snorlax Xander, without a real reason)
I've just begun P. Moon and I've decided to nickname everyone I catch. In the past, I scarcely did that (they are probably less than 10 total in all the games I've played), so I though "let's try this". Though I started to think it's not a brilliant idea when the best (=only) name that came to my mind for a Ledyba was "Bugsy". D: Bugsy the Ledyba .-. god