Does the FCC issue call signs to all users including the federal government?

The Federal Communications Commission (FCC) issues call signs to non-federal users and that is how the stations are tracked. The federal stations could issue their own internationally recognized call signs, but it was decided long time ago to let the FCC do this. By international treaties (the ITU), military departments may depart from the call sign letter and number scheme. That is why a MARS station has a call sign that follows the international scheme whereas a tactical unit or an installation may do something else. Civil Air Patrol follows the procedures and guidance used by most of the Department of Defense (DoD). All CAP call signs are recorded in DoD call sign books, but these books are not normally seen by the general public.

For the general member, all you need to know is that, if qualified, your wing Director of Communications will be happy to help  issue you a callsign.