In the Twilight Saga, why is Jasper's last name Hale?

Hale was Rosalies last name when she was a human untill Carlisle turned her, and Alice and Jasper were already vampires when Carlise found them, they had been travelling together as Alice Brandon and Jasper Whitlock, but he is usually named Jasper Hale which I don't get. I am pretty sure Jasper and Rosalie aren't related at all :P. Thanks xxx