I always name my pokemon, I'll give examples from my party and a couple from my boxes.
In my party:
I have a Pidgeot named Brewster. The first ever pokemon I caught, really.
My Greninja is named Froggy. Probably because I'm a good fan of Sonic and Big the Cat is the best character in fiction. Sue me.
I have a Charizard named X, because...well gee I wonder why, maybe because I'm playing FREAKING POKEMON X? AND HE HAS A CHARIZARDITE X??????
There's also my Beedrill named Buzz Buzz, in which...yep the beetle from Earthbound.
Another one is a Talonflame named Mordecai, and you'll never guess what I named my freakin' Linoone. Go ahead, guess.
Finally, the last one in my party is my Sylveon, which has maybe the weirdest name ever: Applemilk. I don't know why, maybe it's because of that Jaiden Animations nuzlocke video, but other than that, WHY DID I NAME MY FIRST EEVEE FREAKING APPLEMILK???? All the other pokemon have names that are SLIGHTLY connected to their attributes, like, yeah, Froggy is a frog pokemon, Mygrane the Psyduck can get a lot of headaches, and Posiedon, Fiery, and DJ Volt (who are all eeveelutions too btw) are named like that because of their types. (also fun fact, DJ Volt is named after a Jolteon i have irl). So WHY did I name him Applemilk?! Eh, doesn't matter, though, he's still my adorable lil' best friend no matter what name I gave him.
Now for the box examples:
I caught all three Panpokemon, and their names are Mario, Zora, and Olimar. I'll leave it to your imagination which ones are which pokemon.
I named the Absol I found Abby, because that might be the best nickname you can give to an absol.
And we're back to weird names again because I named my nosepass after the funny Dr. Robotnik meme. Why?
I named this Stunfisk I recently caught Pancake. That might also be a good nickname, like, he DOES look like one.
I caught once again another Eevee and named her Kumatora. I named her that since I want to collect all the Eeveelutions, and there I go. She'll definitely be an Espeon, for sure. (No I will not rename her to blaze the cat because that dont make no sense other than the design cuz like Espeon isn't even a fire type)
WHY DID I NAME THIS MANTYKE SANS LOLLLLLLLLL
I named this Ralts Marth because I hope to evolve him into a Gallade.
And finally, Excalibrium of Parfum I, the future greatest sword pokemon in Kalos. No, that's not really his nickname, I just wanted him to sound cool. Also, that's way too long for it to be a nickname, so it'll just be his full name. Also, if you couldn't tell, yes, he is a Honedge, and I plan to turn him into a powerful weapon against Diantha's Gardevoir just in case I lose to her at least 5 times.
Anyways, you can tell I love these pokemon.