I thought it was in an episode of DS9 that his first name was Skrain. I don't know which one though.
All the show ever gave us was one episode where he gave his name--or name and title--it's not clear--as "Dukat, S.G." This could have been "Station Gul," but it's not clear.
"Skrain" comes from the Pocket Books novels.
At first I admit I was not the biggest fan of that name, but I've now spent a few years writing for an alternate "good-guy" version of him, and just the different feelings associated with that character have changed the way I hear the name. When I write the "good twin," I don't hear the harshness of the name so much...I hear the rhyme with "rain." But when I write about Gul
Dukat, it seems like a harsh, mean name to go with a cruel man.