Well, the original name for the FBI back in the day was the
Bureau of Investigation (BOI).
Fun facts, in the video game,
Grand Theft Auto IV, the FBI was referred to as the
Federal Investigation Bureau (FIB), and in the 1990s television programme,
The X-Files, the FBI was listed as being under the fictional,
Department of Investigation (DOI), rather than the
Department of Justice (DOJ) as it is in real life.
Personally, I think the following are possible:
Federal Office of Investigation, using the current formula, X Y of Z.
Federal Agency of Investigation, using the current formula, X Y of Z.
Federal Department of Investigation, using the current formula, X Y of Z.
Federal Criminal Investigative Service, based off of the USN'S NCIS.
Federal Department of Investigative Services, based off of the USN'S NCIS.
Federal Bureau of Investigative Services, based off of the USN'S NCIS.
Federal Agency of Investigative Services, based off of the USN'S NCIS.
Federal Office of Investigative Services, based off of the USN'S NCIS.
Federal Investigation Agency, based off of the DHS's FPS.
Federal Investigation Office, based off of the DHS's FPS.
Federal Investigation Department, based off of the DHS's FPS.
Federal Investigation Service, based off of the DHS's FPS.
Federal Investigative Office, based off of the DHS's FPS.
Federal Investigative Agency, based off of the DHS's FPS.
Federal Investigative Service, based off of the DHS's FPS.
Federal Investigative Department, based off of the DHS's FPS.
Federal Intelligence Agency
Keep in mind that the FBI is more of a law enforcement agency like a jurisdictional police department rather than an overseas intelligence-gathering one such as the CIA or NSA. The FIA would sound more proper as an alternate name for the CIA or NSA.
Government Investigative Service
I see what you did there; very similar to the USN's NCIS.
