he didn't remember his mother, remember? and skywalker would be a very conspicuous name to have if Darth Vader is looking for you, so Padme probably didn't use it. and Luke had no idea about his parentage so he wouldn't care if he used it. or maybe he iddn't like his uncle enough to use his name! who knows?!
Remember, too, that the best hiding place is atop the mantel (something like that). As it's been noted, a Skywalker on Tattooine wouldn't necessarily raise an eyebrow; after all, Shmi had parents, and she could just as easily have had brothers and sisters. Luke could have a dozen cousins.
Vader might have had his troops scour the Skywalker clan on Tattooine once or twice during Luke's childhood (if Tarkin were to allow such expenditures of time and manpower), but even then, he might not have thought to include the Lars farm in that investigation.
Since the tragedy of his mother's death accompanied his first meeting with the Lars family, and he left indefinitely soon thereafter, there's no reason their farm would be foremost on his mind when it came to potential hiding spots.
Besides, he's been too busy in the intervening years attending to Imperial business to devote that much time to looking for his kids; plus, he knows that their paths will eventually cross anyway (the Force works in mysterious ways).