I love this thread!! This is generally something I don't share or get to talk much with other people cuz it's strangely uncommon, but I've loved nicknaming all my team's mons in-game since gen3 or so. I also nickname my competitive teams when I feel I'm gonna save it and use it for a long time.
It makes it easier to remember the mons you've used in the past, but only to a certain extent. In Emerald I remember in my latest run(s) I had my Blaziken named Blaze (so original) and a Gardevoir called Freya for the nordic Goddess.
I sadly don't remember much about my Diamond team besides a Gyarados called SolidSnake for obvious reasons.
Gen5 was the gamechanger for me. It's kind of hard for me to forget my hall of fame entree's nicknames; i dont know if it's cuz it has only been a few years or because I put a lot more thought into them.
- Torchamp the Emboar: Pretty obvious mix of Torch and Champ.
- Vera the Whimsicott: Primavera is spanish for Spring. In fact, it's nickname was Prima at first, but I later changed it cuz I had a cute friend called Vera that I thought matched this pokemon p well.
- Galvani the Galvantula: obviously named after Luigi Galvani the physician.
- Kirikiri the Excadrill. This is the onomatopoeia for a "drilling" sound in japanese.
- Coyfel the Liepard. Just a combination of Coy and feline.
- Yin the Reshiram. Yeah, legendary, whatever. Obvious taoism is obvious. I don't think I used it much in the league anyway :p
I actually had to look for my Black cart to remember the mons after Galvani. I was a lot closer to the first three, really lol.
I also found my 4 main HearGold mons in this cart!
Agnak the Typhlosion (there's a Monster Hunter mon in there that looks like him imo),
Hunter the Gengar,
Ryuusei the Starmie (shooting star in japanese), and
Striker the Scizor. Striker is the jp name for Scyther.
I still remember my X team off the top of my head, but I'll spare y'all that since I played the game in japanese and I don't wanna have to go into a lengthy explanation for their nicknames :p