When Jasper became part of the Cullen's coven, he had to be able to blend in with their human facade. Since they were already telling people that the younger vampires were adopted, they decided to use the same excuse for Jasper. Since he and Rosalie are both blond, they decided to pass them off as siblings and give Jasper Rosalie's surname.

THX A LOT UR REPLY REALLY HELPED

No problem.