Is there only a single Skywalker family?

Main (Disney) Canon.

Only three 'Skywalkers' are mentioned in the main canon and all are direct relatives of each other:

• Shmi Skywalker

                  ↓

• Anakin Skywalker

                  ↓

• Luke Skywalker

Additionally, Rey takes the surname Skywalker at the end of Rise of Skywalker, honouring Luke and Leia's contribution to her training.

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"Legends" Canon

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.

Luke Skywalker.

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 galaxy.

_{^{The Rise and Fall of Darth Vader}}