Because it's a very common name in Scotland. You know, like "Di Blasi" in Norway!
The Stuarts had a credible claim to the crown of Scotland and, indeed, all of Britain. Charles Stuart, aka Bonnie Prince Charlie, was the last Stuart to press that claim; I believe there is a successor to the line yet living somewhere, maybe France. They were Catholic, so their claim was not universally supported in Scotland. But many Scots still remember, or at least buy the romanticization of it all. The gates at Traquair House, the oldest inhabited house in Scotland, have been closed since Charlie's defeat, and supposedly will be opened only when a Stuart again sits on the throne.
I don't know why people name their kids after Scottish historical figures.