[dhosek]

Nope, Stuart was the surname of the kings from James I–James II.

[bell-cot]

But actually, their surname did come from "Steward" -

https://en.wikipedia.org/wiki/House_of_Stuart

And they were monarchs of England, Scotland, and Ireland from King James IV-who-was-also-King James-I through Queen Anne.

[Veen]

James VI and I, not IV and I.

[bell-cot]

Oops! - yes, thanks.

James IV was about a century earlier, and "only" the King of Scotland. But it was his artfully negotiated marriage to Margaret Tudor that set the dynastic stage - for his great grandson (James VI and I) to also inherit the thrones of England and Ireland in the Union of the Crowns.

https://en.wikipedia.org/wiki/James_IV