No you can't not unless your ID Number and Secret ID Number is the same as the player who the traded Pokémon originally belonged to, or the Pokémon is returned to it's original game.
In addition, a traded Pokémon's nickname cannot be changed by anyone but the original Trainer, even if it hasn't been given a nickname.
Traded Pokémon cannot be renamed unless they are returned to their original game; if it is impossible for the traded Pokémon to be returned, it cannot be renamed at all. If 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. Very rarely will two players' numbers coincide; this is the only time when traded Pokémon may be renamed.
Traded Pokémon are identified by the Pokémon's Original Trainer name and a five-digit ID Number. Starting in Generation III, even if two games have the same name and ID number, each Trainer also has a secret ID number. The odds of two Trainers having the same secret ID numbers is 1/65536 or approximately 0.002%, making it extremely unlikely that an outsider Pokémon will be treated as a regular Pokémon on a different cartridge.
Source: Experience and Bubapedia
Hope I helped :)
