No.
Nicknaming Pokemon does nothing to anything unless you are playing Pokemon Red, Blue, or Yellow, where there is a rumored glitch that nicknaming a MewTwo and swimming on the edge of Cinnabar Island will put the sixth item in your bag at the max amount. Other than that, there are no more nickname related events in Pokemon games.
And besides, nicknaming Pokemon is too fun to become complicated with special events.
"I have to nickname my Regice 'Regice'?I must rage quit!"