Short answer: No.
You have to have the same Trainer ID as the person who caught it, so unless you were very, very, lucky, you can't nickname Pokemon transferred from Pokebank.
>taken to a Name Rater, he will say the name is "perfect" and refuse to change it. This is to maintain the unique character given to the Pokémon by its Original Trainer. The game recognizes the trade when the OT number assigned to the Pokémon does not match the number on the save file.
The OT number has to match the Pokemon's and if not the it cannot be changed
