Cooper is a Pokémon coordinator and trainer from Pokemon Iron and Amber and Pokemon Copal. If you choose the female character Amber than she appears as a member of the Elite 4 however if you choose the male character Iron than she appears as your contest rival, always showing up at your contests and challenging you.
When you first meet her as a contest rival and she introduces herself she says that she prefers to be called Coop. When she is met as an Elite 4 member she says that her name is Cooper but that's far too formal and you should call her Coop.
It is implied that Cooper comes from Fiorre, she says that he comes from a desert place where there never used to be any Pokemon when you first challenge her at a contest. During your final contest when Team Rocket interrupts she shouts "Rocket? What about Team Snagem!"
Although it is never stated in the game it is confirmed that Tin is her twin brother, hence why they have such interchangeable positions.