I named my Eevee Ren. ...Mostly named after the anime version of Joker from Persona 5, the "Wild Card" of the party. XD Also in tribute to Joker coming to Super Smash Bros Ultimate as DLC.
I originally named my partner Eevee for Let's Go Vee after Red's Eevee. Now I call him Riki after my favorite Xenoblade Character because it gets a move exclusive to it for each of Eevee's evolutions. My Partner Pikachu in Let's Go? I originally called him Pika, after Red's Pikachu. For now, I' m calling him Rai because it means thunder.
I named Eevee failure, and me and my rival are also named failure. Fun fact: if you and your rival share the same name, whenever your rival uses a healing item, it will actually say "You used a (item of choice)!"
Whenever I get the game, I guess I either call my Eevee, Hao or leave the original. as mostly my eevee evolved into umbreon. But I am uncertain so far
If I ever do eventually get the game, I'll name my Eevee Verity after the Eevee starter an old OC of mine had, which also happened to be an Eevee that wasn't able to evolve. Woah, really? GG, you found a funny glitch!
I didn't name it on my main file but in the nuzlocke one I named it Diva because it was the first thing that came to mind.
Lately, I've themed my Pokémon profiles after Buffy The Vampire Slayer and Angel. My trainer is Angel and my partner Eevee is Cordelia.