In "Twilight", why do Jasper and Rosalie use the last name Hale instead of Cullen like the others?
I think the reason why Rosalie and Jasper have different last names is because each is romantically involved with one of the other "foster" siblings. Remember that Dr. Cullen created his "family" by either turning other people into vampires or accepting existing vampires into his group. Because vampires don't age physically, they continue to look the same as they did when they were "turned" (that's one reason why they are so against turning small children into vampires). Because they want to assimilate into human society, the younger Cullens all attend high school. If they were all named Cullen, it would be more difficult for the human teenagers to accept that brothers and sisters--even though not related by blood--were dating each other.
If they use the same last name then it would look really weird if they all have the same last name when Rosalie and Emmett and Alice and Jasper are a couple. Also Rosalie wanted to keep her last name and Jasper could pass as her brother which is why they kept it that way.
Jasper uses the last name of Hale because he and Rosalie look so much alike and people assume them to be twins. The vampires tend to go with whatever the humans are willing to believe. Rosalie insists on using Hale as a last name, and therefore, Jasper took it as his, too.