Main (Disney) Canon.
Only three 'Skywalkers' are mentioned in the main canon and all are direct relatives of each other:
Excluding relatives of Shmi, it would appear that there are indeed other Skywalkers, potentially even some living on Tatooine (at least according to Vader).
According to a captured Rebel whom Darth Vader interrogated on the
planet Centares, that was the name of the X-wing pilot who had
destroyed the Death Star.
Even while inspecting his nearly completed flagship, the Super Star
Destroyer Executor, at the Starship Yards of Fondor, Vader could not
get Luke Skywalker out of his mind. He silently chewed on the name,
and considered the fact that the boy had been born three years after
the death of Shmi Skywalker. To the best of his knowledge, Anakin
Skywalker had been his mother's only living blood relative.
Could there have been other Skywalkers from Tatooine? Vader allowed
the possibility. After all, it wasn't an entirely uncommon name in the
The Rise and Fall of Darth Vader