In Forks, the story that the Cullens are keeping up is that Rose and Jasper are twins, so that's why they're using Rosalie's last name from when she was human, which is Hale.
it's part of their little cover-up-the-fact-that-we're-really-vampires scheme. jasper and rosalie looked alike so they decided that they would say they were twins.
As I re-read page 18 as one person said, it never alisema anything about them looking like twins. In fact quote (from page eighteen paragraph three) "They didn't look anything alike". Jasper Whitlock Hale Cullen is his name. Whitlock is his middle name. In none of the vitabu does it claim they pretend to be twins. People got that from an interview from Jackson Rathbone saying he, quote, "Tries to be Rosalie's (Nikki's) twin". Judging from Rosalie's story and Jasper's it's distinct that they are not from the same time frame. Simply because Jasper is most likely the oldest (since they don't know 100% when Alice was born). Carlisle was zaidi than likely born in 1870s. Jasper was born in the late 1850s. Rosalie, since they say Edward was already with Carlisle when Carlisle found her, was born in the 1900s. In La-men's term, Jasper was born roughly a century before Rosalie. And they never claim to pretend to be twins.
So they have the same last surname zaidi than likely distant relatives. Perhaps he's her great-great-great uncle. Meyer never makes it clear.
They are not actually brother and sister the last name Hale was Rosalie's when she was human so she kept that and when Jasper joined the Cullen's they decided to give him that last name for part of their cover story.