I usually don't nickname my Pokemon, but once in a blue moon I just spontaneously go with it. Usually these are Pokemon designed for specific roles, e.g. breeding, training, HMs, etc.
Most recently I nicknamed a perfect 6IV Adamant Smeargle (moveset: False Swipe, Spore, Soak, Simple Beam) I bred for catching purposes "Happy Trees." Anyone who was on the Bob Ross train would know.
I have a Venasaur I use for spam horde EV-training (moveset: Earthquake, Petal Blizzard, Sweet Scent, Protect) nicknamed "Effortsaur." Ultimate creativity >_>.
I have a perfect 6IV Adamant Talonflame I use for egg-hatching nicknamed "Incubatress" considering she's essentially a portable incubator.
I have a Noivern I use specifically for spreading Pokerus... and it's nicknamed... "Pokérus." Whoopie >_>. I have a ton of other Pokemon currently infected with Pokerus, but it's easier for me to just stick with one to do the happy disease spreading.
I also have an army of Dittos named after their natures: Adaman-Dit, Mod-Dit, Jolly-Dit, Timi-Dit, Hardy-Dit, Imp-Dit, etc.