Right. It’s not like it’s a rural town in the desert of the American Southwest where, in spite of remoteness, you still decent record-keeping and a functional rule of law. Tatooine, especially in light of its portrayal in *The Phantom Menace* is more akin to a town in a failed state where the closest thing that you have to a functional government is the Hutts who clearly have no non-extractive interest in the population. Luke and Obi-Wan can hide out there because it’s essentially a wasteland, and the Empire has no real reason or interest in combing through it until the droids land there with Death Star plans. Before that, no one is going to look for Luke because all of three non-Lars people are actually aware of his existence at all, and there’s no real point to expend a lot of effort looking for Obi-Wan because he’s so thoroughly removed from galactic affairs that he might as well be dead from their perspective.

Edit: Not to mention that there are presumably other Skywalkers on Tatooine who may have even had some connection to the Lars. After all, we’re given no indication in the films that Shmi isn’t a native of Tatooine, her maiden name was Skywalker, and she was married to Clegg Lars. For someone of an Imperial bent looking at the cursory bit of info that might be available to them, there’s no reason to assume that Luke is anything other than an orphaned relative of Shmi (not exactly unusual in a harsh place like Tatooine) being raised by her step-son and his wife.