I find that I alternate between my teams having a consistent theme, only certain team members having a theme and not having a theme at all. Nicknames as a whole are important to me because I feel like they give the Pokemon some sense of character and make them feel real? I'm not a roleplayer and I do not have an OC (I wish I did though, it seems so fun! Guidance on doing so is welcome) but having my player character feel like an actual person and the Pokemon they use feel like a genuine team member and part of a squad makes the file more fun for me. Themes can make a whole team work cohesively, whilst random names actually make the Pokemon themselves stand out a little bit more. Funny how that works.
Sinnoh:
(Royal ~ Bandit ~ Amaterasu ~ Titan ~ Virtue ~ Raijin)
This is my Brilliant Diamond team... that I haven't yet beaten the game with yet. This line-up has a partial theme with Magmortar (Amaterasu) and Electivire (Raijin), named after Japanese deities. It works really well - Electivire looks and feels like a thunder god, and Magmortar is the natural counterpart to Electivire so it needed a name of equal standing. Empoleon is named Royal to reflect the colour (royal blue) and its appearance (it has a royal appearance). Roserade is named Bandit due to the masquerade mask, Togekiss was named Virtue because it looks like a pure being, and Rhyperior is named Titan because it kinda fits the Greek myth but mainly because it's big and strong?
Johto:
(Chomper ~ Dumbo ~ Darren ~ Vengeance ~ Hercules ~ Halo)
This is my Crystal team from late-2020, which has no themed nicknames! The names mostly fit - Feraligatr's main theme is biting so Chomper works, Donphan is an elephant so Dumbo makes sense, The Batman had an awesome trailer come out around then so Crobat was named Vengeance in support of that, Heracross is designed from a hercules beetle and Umbreon has halos on it (plus I always name Umbreon Halo, from way back in 2010 in my first HGSS playthrough). The only weird one is Darren the Dunsparce, named because my roommate at the time thought it was funny - it was his idea to use it after he bet I'd find one instead of the Teddiursa I was hunting, and thus Darren became a meme in my house.
Hoenn:
(Poseidon ~ Athena ~ Ares ~ Zeus ~ Hermes ~ Hades)
This is my Sapphire team, named after the Greek gods! I was going to do the Roman equivalent in ORAS when I got around to playing it, but I'd stopped my "beat every generation" run by the time I hit Gen IV. The names fit the Pokemon well, do I need to explain them? Breloom was named Ares over Demeter or Persephone (the more Grass-type fitting names) because I was not intending to use Breloom as a true Grass type in this playthrough, but that's the only one with a nickname you could maybe question.
Kanto:
(Huu ~ Bumi ~ Pathik ~ Paku ~ Koh ~ Azula)
(Iroh ~ Momo ~ Yue ~ Toph ~ Bushi ~ Appa)
These are my Kanto teams! The top team is from Red, the bottom team is from LeafGreen. Both have nicknames based off of
Avatar: The Last Airbender and a future Let's Go team would have continued that theme (or maybe diverged into
Legend of Korra nicknames). Why? I was watching the show at the time at the behest of a friend, think I finished the show by the time I'd beaten LeafGreen. Again the names make sense if you watched the show, I think the only niche ones were the Grass type names (Huu was the swampbender, Bushi was the name of that weird dude from the Painted Lady episode) but everyone else makes sense.
As for the future, I'm aiming to clear my Pokemon games on my Switch before Scarlet/Violet come out - Brilliant Diamond, Sword/Shield, Let's Go Eevee and Legends: Arceus. I think at the moment my thoughts are to either keep the same semi-themed names from Brilliant Diamond across all games, or to have no theme at all and just name the Pokemon after what I think fits them in my head at the time? But we'll see, plenty of time to decide that (BDSP is far from finished for me).