To borrow from Star Trek, I like the idea of the Romulan Intelligence Agency, The Tal'shiar. A government agency almost more powerful than the government themselves, and often doing things that could be seen in direct conflict with the goals of the government and the military all due to constant suspicion. This could fit such a theme very nicely as an empire in decline might be suspicious of even their own military and government leadership. By the way I'm not suggesting using the name, just maybe if you were looking for a motivation for such a force.
If you invent the whole abbreviated history of this empire, think of a name that fits in with the history. As you can see with my example, it doesn't have to be a name that sounds like Defense this or Force that. Sometimes a name that evokes a thought of suspicion and espionage or mystery and deadly purpose can do nicely.