Where can I change my Pokemon's nickname?
In the previous generations, there was a Name Rater who could help you change your Pokemon's nickname, unless it was traded. Where is the Name Rater in this generation?
Talk to the man in the Pokemon Centre at Camphrier Town. When you enter the building, he's on the right side.
He can change your Pokemon's nickname, the same as any other generation (I presume so, as you have described)