“If Anakin is from Tatooine then wouldn’t that be the first place he’d look for Luke?”
I was thinking about this recently… the OT is pretty vague about Luke’s relationship with his Aunt and Uncle, so it can be resolved without necessarily contradicting anything official. Who are they actually related to in your rewrite? Are they important characters or just in the background? If you remember, no one ever calls him SKYWALKER until he introduces himself to Leia on the DEATHSTAR. What if he was always told he didn’t need to know about his father… He was a Lars now (sounds like something Owen would say)? What if… that moment Luke says “There is NOTHING for me here now. I want to learn the ways of the force and become a Jedi like my father,” is the moment when Luke decides he will NOW go by his father’s name? Just an idea.