If they were so intent on keeping him safe and hidden from Vader and the Emperor, you would think that's one of the first things they would have done, especially after Obi Wan went to all the trouble of relocating him to Tatooine, one of the most remote planets in the galaxy. If Vader and Palpatine had any suspicions regarding any offspring from Padme, one of the first things they would have done is search the Galactic yellow pages for any Skywalkers, just to be safe and cover all their bases. Unless Skywalker happened to be the most common surname in the galaxy, kind of like Johnson or Smith, so it would have been a ridiculous waste of time and unrealistic for them to hunt them all down and interrogate them.

Leia took on the last name of her adoptive parents. Why not just call him Luke Lars, just to be safe? Why take the risk of him being discovered? It would have been such a small thing to change his last name. It's one of those things from Star Wars that doesn't quite make sense.