When I first began playing the pokemon games, I very rarely gave my pokemon nicknames. Pokemon were pokemon, and I was more giddy about the fact that I was actually owning a game going about catching them all, and so I just left them with species names. My best friend in elementary school, however, was just the opposite. She nicknamed every pokemon except legendaries (because those are unique? I guess), even naming her starter swampert after me.
She must have rubbed off on me, because some time around the fourth generation, I pulled a 180. Everything I caught was nicknamed. EVERYTHING. And since I am always compelled to capture every single available species, each one of those eternally-boxed trash'mons has a name. If there's a typo in the name as I type it, I leave it in for laughs. By the end of the run the names are no longer scraping the bottom of the barrel, but have broken through the floor and are digging into the ground.
Post-game nowadays, every 'mon on my team I try to come up with a good name for, since others will be seeing it, but after going through the story and having caught them all and given them dumb monikers like "adiowx" and "Potato", I cool down on nicknaming anything but deliberately bred for team members. Especially when breeding. You'd have to be some special kind of mad to try giving a name to every child in the boxes of imperfect hatchlings.