Taken from Facebook as to why Cauis calls Lightning everything but her name:
He doesn't want to get personal with her. They are supposed to fight each other to the death, not be all buddy buddy. Once he calls her by her name, he's sunk. He'll think of her more than just an opponent. She'll be a living breathing person to him, and he's scared of it. But he wants to call her by name, and that scares him even more.