I hope not! Sawney is a Scots version of Sandy, itself a shortened version of Alexander, so perhaps it was in common usage, but I have only found three examples of the name, and the stories that go with them are certainly not fairy tales.
SAWNEY BEAN was reportedly an incredible monster who, with his Wife, lived by murder and cannibalism in a cave. He was executed at Leith along with his whole Family in the Reign of James the First.
SAWNEY CUNNINGHAM was an abandoned villain who inveigled and murdered his Wife's lover, murdered his uncle, terrorised the country-side. He too was executed at Leith, 12th of April,1635
was Scottish highwayman who laid England under toll, and took a copy of "Chevy Chase" to Tyburn when he was hanged on 10th of September, 1664.
He is one of several rogues and vagabonds
who have their place in the Douglas Archives. If you know of any more, we would love to hear their stories.