Why is it that Rosalie is a Hale but she lives with the Cullens?

because she looks like jasper and they thought if they had the same last name the other people would assume they are twins.

well look at it this way
Emmet and Rosalie are dating and they have the same surname, people would assume they are biological siblings. some people already think it's weird that they live together.
so of course she has to have a different surname,
as for the Jasper thing- like the other usser said, Rosalie and jasper look alike, people assumed that they are twins and Rosalie had no intentions of changing her surname, so Jasper had to change his to Hale.

Look Rosalie her humand last name was hale she didnot want to changed so she stay with hale she lives with the cullens cause she is marry to emmett.

because she wants to and no one is stopping her from leaving if she wants to but even though she wanted to grow old and have a family i guess that they are the only family she has

She lives with them because on the night of her last araw of being a human, her husband to be raped her or something like that and Carlisle found her. She thought he was hepling her but he bit her instead and offered her a tahanan with him. Oh and of course that's when she met Emmett. Also, she didn't even want to be a vampire bit now she can't change back.

Everyone is right, It is also in twilight,Esme is their"Aunt".Jasper and rosalie have the same last name because they are close and look like Twins.It would be weird if she was a Cullen to humans.

They don't want to claim that all five younger Cullens were adopted sa pamamagitan ng Carlisle and Esme, because it would seem strange that such a young-looking pair had already adopted so many, and it would also make the pairings appear incestuous. So they claim that Emmett, Alice and Edward are siblings who were adopted together, and that Jasper and Rosalie are Esme's niece and nephew. Hale was Jasper's human surname.