Star Trek is really inconsistent with the names they use. Also, let's not forget the time Picard set a course for the "Klingon imperial Empire." It's not just Star Trek, though. In Babylon 5 the Narn, Centauri and Minbari are all referred to as an empire at one point or another - even though the proper titles are Regime, Republic and Federation. And, aside from the Narn Regime, their titles don't make much sense either.
EDIT: Also, think of all the times Federation officers referred to the "star fleet."
As for Dukat and his title of Gul, I could go off on a completely different rant about the subject, but let me say this. First, I think that the title had become so intertwined with his character they just forgot about that fact when he took over the Cardassian government. They only got around to correcting that mistake when Damar was made the leader of Cardassia. I never saw Dukat as the modest type, and feel like he would try to amass a Kim Jong-il level of titles the second he grabbed power.
Second, why the hell didn't they give Dukat and Damar first names? Dukat is referred to as either Dukat or Gul Dukat, and in some conversations it just sounds hilariously inappropriate and awkward. Sometimes it's as if Gul isn't a title, but his first name. I mean, I realize that 99% of the time he refers to Sisko as Commander or Captain, but in some conversations the lack of a first name for Dukat makes referring to him as Gul Dukat just sound goofy. Also, Skrain was a great first name for him. Kudos to whoever came up with it (S.D. Perry or Andrew Robinson?)
Do you know what it's like to fall in the mud and get kicked... in the head... with an iron boot? Of course you don't, no one does. It never happens. Sorry, Ted, that's a dumb question... skip that. - Captain Rex Kramer
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L.A. 15, 7 Adam. 10-5 to Mary 3, I've got a blue van in the RV storage lot, 1600 North Willow. 10-35, 7 Adam is rolling.[This message has been edited by Viceroy Billy (edited 01-23-2015 @ 10:10 PM).]