Dad's Government Business, or more exactly the acronym DGB, is a name Edward Verres uses to tell his son that something is part of the classified work he's doing for government. The real name and structure of the agency is never specified in story, but Edward is mentioned to be head of paranormal division up to the end of Sister II (then "promoted" to head of paranormal diplomacy) and the other agents claims to work for FBI, so it is most probably paranormal division of FBI.