Apparently you can name the office without naming the person (so, defendants would be Attorney General of the US, not Eric Holder). You wouldn't name the DA as she doesn't have anything to do with the agencies dealing with your case. The District Director of CIS is a different story.
By the way, some people have even named the president as a defendant as he is the head of the executive branch that oversees the departments and its agencies.
Whatever you choose to do re the FBI checks, you can explain that you are getting conflicting responses, and there seems to be no coordination within the agency, which could indicate a lack of service or professionalism for which they charge the fee of $590 or whatever. In the end, they know they have 120 days to adjudicate before you can sue, and if they think think they can't make it, they should know where they stand and for what reason, and that they should contact you to explain/request additional information.