Most of mine name their aces, but I just wrote out 14 nicknames for renahv pokemon.

Outside of their actual nicknames Odd's given his team, some other examples are;

Mauve: "Your Majesty", Ms. Daisy, A Chara

Barb: Nibbler, Sweet Tooth

HAL: Magneto, DJ Drone (that has some history to it)

Joseph: Jaws, Fishman

Yggy: Green Giant

Kat: Sealgaire (also used by Odd's dad)

The a bit of a spectrum when it comes to my OCs' nicknames for their pokemon. On one end you have Mary's Gourgeist, that she named Jackie...you can probably guess where she got that name from. And then there are less diegetic picks like Jin's shiny Gyarados Ao Qin, who I named after the crimson dragon king of the south sea, but Jin just named him that because she thought it fit him.

I love love this qn lunya AAA

Kingston's initial team: Mercedes, Cooper, Vespa (and i forgot the rest) were named after car brands... and his current ghost team were named after ghibli characters: Calcifer, Sophie, Kohaku, Moro, Eboshi

Ruth's team: Mila, Aquilla, Faelan, Lyall (just naming them what sounds nice)

Mira's team: I have no idea YET, I might name them after classic book characters QWQ

Balei nicknamed her Kommo-o Harlem but sometimes calls her Happy Feet!

Fausto’s Excadrill is name Tekken but sometimes he calls him Kenny, and Anthem the Tyrantrum was givin the second name of Fur Ball :)

Picking one from each Character I have nicknames done for:

Wily: Type-1 (Type:Null)- Usually shortened to T-1. Wily didn't want his name to basically mean "valueless" and it's a T-1000 reference.

Polly-Gramps(Spiritomb)-Her family 'made' it by assembling the required souls, and the main soul in control is literally one of her ancestors. (A great-great grandfather)

Mahra - Sundae(Alakazam):Because of the spoons and it has a sweet tooth.

Child Pace creatively named a Munchlax "Pancake" after feeding it pancakes sdfghfd the nicknames of his other Pokemon are also food/utensil related, such as Bib the Cramorant and Pin the Eiscue

Cecils got a lot of nicknamed boys! Not very creative mind you!
Hopper - Named after how he hops along
Bubu - Angry lil guy who'll leave you with "Boo Boos"
Herb - Weed reference
etc...