I don't now where to change one Pokemon's nickname.
You find the name rater inside the Medal offices.
You can find the name rater on the ground floor of the medal offices in Castelia City.The medal offices are on the left-most street and in the first buiding to the left.
You can change its name in Castelia city on the left street he is on the right side of the bottom floor.
note you cant change the name if it is a traded Pokemon.