Why didn't Obi-Wan or Owen Lars change Luke's last name?

The novelization of Episode III makes it clear that Anakin was known as a galaxy-wide hero on the HoloNet, and that he had become a household name.

Why did Obi-Wan and Owen Lars, when making the handoff of Luke, change Luke's last name? Even on Tatooine, a lot of people would probably recognize the name Skywalker. Some especially curious people could have done some basic detective work and figured out additionally that Luke's guardians were related to Anakin Skywalker's family.