I've played six main series games ever since I finally got good at Pokémon years ago: Pearl, White, Black 2, X (which I've raised two teams in), Alpha Sapphire, and HeartGold (during a bit of a retro kick). However, I didn't do much nicknaming at first; I'd give the occasional name when I came up with one, but it wasn't until X that I decided to give names to my teams as well. And here they are:
X - Main Team
Fyraga, Delphox - Named for the fire magic from Final Fantasy, with a y in place of the i because I thought it looked mystical
Bugzzy, Diggersby - At first, a reference to Bugs Bunny, but then I spelled it like the Kirby character because I could
Bulblax, Venusaur - A twofold reference to Pikmin; it's a direct reference to the massive Emperor Bulblax boss, and a nod to the Pikmin and the Bulbasaur line both being plant/animal hybrids
Bluebell, Florges - Very simple; a blue flower Florges, named for a blue flower; I gave similar flower names to the other four colors of Florges as well
Muramasa, Aegislash - A reference to the mystical katana, Muramasa
Everest, Aurorus - Named for the great mountain, since Aurorus is a huge Rock/Ice type
X - 2nd Team
Woofer, Noivern - Named for the large, bass-y type of speaker
Eggplant, Gourgeist - I named him Eggplant because he's shiny, and shiny Pumpkaboos/Gourgeists are purple instead of pink-ish orange
Casey, Alakazam - I gave him the name as an Abra, because I saw that it was Abra's Japanese name and found that quite amusing
Filia, Mawile - Named after the main character of Skullgirls, who has a similar head mouth in her hair named Samson; if this Mawile I caught had been male, he would totally have been named Samson instead
Goosey, Barbaracle - I named him after a variety of stalk barnacle called the goose barnacle
Jet, Pangoro - Pangoro's gangster-ish looks reminded me of West Side Story, so she got named for one of the gangs in that play
Alpha Sapphire
Gex, Sceptile - Named for the title character in the Gex games
Scarfy, Linoone - Since he's shiny, he's bright orange; between that and the Silk Scarf he's equipped with, I decided to name him after the Kirby enemy
Famalia, Sableye - Named for a magic spell from Layton vs. Wright, which can summon a ghostly familiar; after learning about Sableye's design origin, the Hopkinsville Goblins, I decided that if I ever raise another Sableye, it will be named Hopkins
Rollo, Azumarill - I honestly don't remember why he's named Rollo; probably something to do with the Marill line's roundness
Vesuvia, Camerupt - Named after the notorious Mount Vesuvius, although I changed to a feminine suffix since I caught a female Numel
Ruby, Latias - Given the games' names and her red coloration, the name Ruby occurred to me instantly; after catching her counterpart later on, I named him Sapphire to match
HeartGold
Lightan, Typhlosion - After naming the protagonist Gold, I named my Cyndaquil Lightan as a reference to the odd and obscure Gold Lightan
Happy, Togekiss - Named after the character from Fairy Tail, because Togetic reminded me of him for some reason
Prince, Nidoking - Named after the artist formerly known as "The Artist Formerly Known As Prince", because of his purple coloration and the presence of king in his species name
Nieve, Glaceon - Another simple one; nieve is the Spanish word for snow
Faraday, Magnezone - Named after Michael Faraday, inventor of the Faraday cage; doubles as an Ace Attorney reference
Stella, Starmie - An actual name, derived from the root stell-, meaning star
A couple of other nicknamed Pokémon include a Masquerain named DeMasque (another Ace Attorney reference), and a whole alphabet of Unown that each have a name starting with the letter they resemble. My apologies to anyone who doesn't like massive posts, but I just felt like sharing and got carried away.