The emperor needs a "right hand" to do its bidding, so I would pick something with "hand". Perhaps "Hand of Imperial Justice"?
Yes... Something along these lines, it's within the mood. I mean "police" sounds very unfitting for such game, it sounds too democratic Imperial enforcers, department of imperial justice, something like that.
I was thinking how to deal with juidical system and police, and yes, I guess joining them together into one "something of Justice" is the best (especially since in a game where you are supposed to run an empire you don't need/want soo much details of that sort).
They could employ:
- enforcers (policemen)
- investigators (detectives)
- arbiters (judges)
As for "hand" I think it should be reserved for individuals, like powerful the most trusted individuals that oversee the things in the empire, especially things that deal with loyalty, corruption, treason. I would rather not call the whole juidical system/brach/service as a hand.