I only nickname the ones I plan to keep in my party.
Sometimes, when I'm feeling immature, I nickname the Pokemon that I trade to NPCs, for example I caught a Bellsprout and nicknamed it VaginaFace, then traded it for the Onix in Violet City. I also nicknamed the Drowsee, that I traded for Machop, my bitch, it was kind of funny to see "Take good care of my bitch." What can I say, sometimes I'm just feeling silly.