No, you can't!
If you want a new name for the Player, you must delete all your data and start a New Game game.
If you have important Pokemon on it, you will need to transfer them to another game or they will be deleted!
How you delete your data?
You can delete saved data. According to the in-game manual you have to "Press up on the D-pad + B + X simultaneously from the title screen" in order to erase your data.
Hope this helps!