I saw this question pop up and realized 'The Dragon and the Rose' could be a few things—maybe that old historical romance from the 80s by Patricia Veryan? Or a fanfic title? Since I'm not totally sure which one you mean, I'll talk about the one I know, which is a medieval-ish political romance. The central duo is definitely Eleanor, the 'Rose,' a noblewoman from a rival house, and Alaric, the 'Dragon,' a warlord from an opposing kingdom. Their marriage is a forced alliance to end a war, so the whole story is them navigating court politics and their own simmering hatred that slowly turns into something else.
Besides them, you've got Eleanor's younger brother, Cedric, who's a bit of a hothead and keeps trying to provoke Alaric, almost restarting the conflict. Alaric's right-hand man, Gareth, provides a lot of the drier humor and practical advice. The main antagonist is probably Lord Merton, Eleanor's scheming uncle, who stands to lose power if the peace holds and works in the shadows to undermine it. The character dynamics are very much about shifting loyalties and the personal cost of political games.