The members of the Cullen "family" are trying to keep up the pretense that they are actually related. Edward, Alice, and Emmett took on the name Cullen when they were "adopted" by Carlisle and Esme; but it would be creepy for Alice and Jasper (and Rosalie and Emmett) to have the same last name, since they're together romantically. So Rosalie kept her original last name and they pretend that Jasper is her twin brother, hence his last name.
The whole reason is so that they can be in public among regular humans and seem like their story is realistic, that they were all adopted by the Cullens so they're a family but not actually related.
Rosalie wanted to keep her last name when she was turned into a vampire. Jasper also kept Rosalie's name because they are like siblings and it would raise less questions if Rosalie and Jasper have the same last name since they can pass off as siblings. However, Jasper, Alice, Emmett, and Rosalie cannot all have the same last name because Jasper and Alice are a couple while Emmett and Rosalie are a couple
They all have the same last names because they were "adopted" by the Cullens and keep a pretense that they are siblings. However, in reality Emmett and Rosalie and Alice and Jasper are couples so they cannot all have the same last name. Because of that Rosalie and Jasper have the same last name Hale in order to not raise suspicion as well as date their significant other.
when carlisle was changed his name was 'cullen'
when he changed edward he became a cullen also.
esme became a cullen when she and carlisle got married
rosalie origanily had 'Hale' as her last name and when carlisle changed her he had intended on edward and rosalie being together.but she found emmett and he became a cullen so they could be together.
when jasper and Alice came to live with carlisle they made alice a cullen and jasper a hale so rumers didnt start bout them being siblings and going out.
so rosalie and jasper ended up being the only two Hales. iguess if there was another one after Breaking dawn bella would also be a hale.
because Emmett and Alice are cullens and people know that emmett and rosalie are together and that alice and Jasper are together therefore If they all had the same name people would think they were..... well you know
None of the cullens are related in any way! Rosalie's name as a human was rosalie hale, and jasper was known as jasper whitlock. As they are all posing as foster children, they take on the appearance of being related in at least some way. Alice, edward and emmett have taken on carlisles last name and rose and jaz pretend to be twins (which as beautiful blondes they can do), hence keeping rosalies last name. Jasper is simply named hale so that the foster children story seems more realistic.
Rosalie and Jasper are brother and sister. Emmet and Rosalie are "married" only half the time, so Rosalie did not take his name. As for Alice and Jasper, they are never married, so they remain Alice Cullen and Jasper Hale.