Elizabeth Stuart, Countess of Argyle - STEWART v STUART

Justin Scott makes a fair point concerning the surname of Elizabeth, Countess of Argyll. Setting aside his explanation for the first appearance of the surname Stuart to Scotland for the moment, his message begs the following question: Should the Geni World Tree identify this woman as a Stewart, or is there a case for regarding her as a Stuart?

Darryl Lundy identifies her as Lady Elizabeth Stuart, daughter of John Stuart, first Earl of Lennox and Margaret Montgomerie. http://www.thepeerage.com/p10921.htm#i109206 Other explanations are possible, but he may only have done so in order to distinguish between her and her sister of the same name, who is identified by him as Lady Elizabeth Stewart, daughter of John Stuart, first Earl of Lennox, and Margaret Montgomerie. http://thepeerage.com/p522.htm#i5219