Mr. Cavendish, I Presume by Julia Quinn

Amelia Willoughby has been engaged to the Duke of Wyndham for as long as she can remember. Literally. A mere six months old when the contracts were signed, she has spent the rest of her life waiting. And waiting. And waiting . . . for Thomas Cavendish, the oh-so-lofty duke, to finally get around to marrying her. But as she watches him from afar, she has a sneaking suspicion that he never thinks about her at all . . .
It’s true. He doesn’t. Thomas rather likes having a fiancée—all the better to keep the husband-hunters at bay—and he does intend to marry her . . . eventually. But just when he begins to realize that his bride might be something more than convenient, Thomas’s world is rocked by the arrival of his long-lost cousin, who may or may not be the true Duke of Wyndham. And if Thomas is not the duke, then he’s not engaged to Amelia. Which is the cruelest joke of all, because this arrogant and illustrious duke has made the mistake of falling in love . . . with his own fiancée!