Competatively speaking, no. A moveset can be proven and tested to be good. A moveset can be good, bad, dumb or amazing, and depending on what it is, it will affect the outcome of the battle.
Nicknames however, are purely cosmetic. Some might be better or worse than the other, but ultimately it doesn't matter. A Pokemon named Bill, %!!! {3pIka@}€ or The Pikanator have the same stats and resistances. It's the same Pokemon.