Why is jasper known as jasper hale instead of jasper cullen? Isn't hale rosalie's surname?

yes

The stoty they put off to the humans, is Rosalie and Jasper are twins... thats why they both have the last name Hale. The story is that they're Esme's niece and nephew that came to live with them after their parents died. Plus it would be a little weird if eveyone had the last name cullen and they were all dating each other....LOL!