He has the last name Hale cuz he looks similar to Rosalie (cuz they both blonde) and the Cullens thought that having them as twins would be less suspicious. And also if he took the last name Cullen, he would have the same last name as Alice and seem more like her brother to everyone! and that would just be plain weird!!

In the books, they say that the human role, is he's Rosalie's twin. And since Rosalie is the more dominant (or pigheaded) she wanted to keep her last name. Jasper didn't mind, so he took her name. They do both look alike, with the blond hair. His real last name is Whitlock. (You find this out in Eclipse) And if his last name was Cullen he couldn't very well be Alice's boyfriend in front of the humans now could he? No. So he's a Hale.

Hope this cleared things up for you.

Jasper/Alice and Emmett/Rosalie couldn't be together if they had the same names, because it wouldn't work that they like eachother when they are all related.