In the Radio Drama, Obi-Wan even says to Han Solo that he hasn't touched money in a long time and has been making his way on his own for some time.

I take that to mean he has no official presence on tatooine.

Plus let's be honest, rim worlds don't exactly have good, robust governments that keep track of everyone. They made that clear early on. You can patrol the streets of major cities and their space ports, but without a major presence, the empire has no idea who lives where in the outer rim.

Plus "Skywalker" would definitely be a common name given how historically on earth a lot of last names correspond to trades and careers, so a "Skywalker" was descended from someone who got their name piloting, or generally being someone who spends a lot of time in space.

So combine all those together with the characters being on a planet that Darth Vader has every reason to hate and disregard, (he was a slave there, his mother died there and he feels responsible, and also... Sand...) the empire could comb the desert and not find shit.