After Revenge of the Sith when Luke and Leia are born, they are hidden so that Darth Vader, their father, won’t find them. But, they changed Leia's last name because she was adopted by Senator Organa and his wife so they changed hers to Leia Organa. I know that Luke was adopted by his aunt and uncle but still, why wouldn’t they change his last name? Skywalker wasn’t a very common name then so if Vader ever heard of a Skywalker living on Tatooine, he would most likely suspect something.
So why not change Luke’s last name so that all of any suspicion could be avoided?