In my head canon it goes like this: Anakin was born with no last name, on the spice mining world of Kessel. He fled an abusive father to make a living in the underground racing circuits of various Outer Rim worlds. On several different occasions, Anakin would land on a world, adopt a racing name appended to his first name ("Anakin Sunrider", "Anakin Starkiller", "Anakin Farlander", etc.), blast the local competition out of the water, and then the local crime lord would try to pay Anakin to throw a match, but Anakin's honor got in the way of that so he would win the match anyway...this would cause the crime lord to send assassins after Anakin, who would hop another freighter, go to another Outer Rim planet, and repeat the whole thing all over again with a different racing name. One of Anakin's many racing names was "Skywalker", and it is of course the one that gets passed down to Luke.