Dame was a designation given to people who belonged to the Garwian Unity nation, which existed within the Unknown Regions. During the High Republic Era, Veermol Tarkin, a member of the Tarkin family, possessed the title of Grand Dame. The Garwian artisan named Mimott also held the title of Dame by the time 19 BBY arrived.
The designation of Dame was first seen in the 2020 novel Thrawn Ascendancy: Chaos Rising, which constitutes the first book in Star Wars: The Ascendancy Trilogy by Timothy Zahn. In our own world, a dame is a title of honor.