Deadheading pilot reports Cabin Attendant announcing the presence of an FFDO on the flight over the public address system before passengers boarded; but while cleaners were still on board.

Narrative

I was assigned to deadhead on this flight; and WAS NOT a part of the flight crew. After boarding the aircraft; and while the cleaners were still onboard; the 'A' flight attendant announced over the public address (PA system) that the First Officer assigned to fly the flight was a Federal Flight Deck Officer (FFDO). All of the cleaners heard the announcement that we had an armed pilot on board the aircraft. This announcement should have been handled with the crew interphone; so the flight attendants in the rear of the aircraft could have been notified without notifying the other personnel onboard the aircraft. In addition to this event; several weeks earlier; while accessing my flight and passing the agent at the podium closest to the door to the jetway; she turned towards me and announced; 'you have one FFDO and 2 FAMS (Federal Air Marshals) on board.' She announced this in front of a line of people she was checking onto the aircraft. In each instance I had to cut her off in mid-speech to prevent the FAMS or the FFDO being made public. Obviously; in both instances; the Flight Attendant and the Gate Agent do not recognize the importance of maintaining the covert nature of Law Enforcement Officers; Federal Flight Deck Officers and Federal Air Marshals that are assigned to a flight. An URGENT or EMERGENCY BULLETIN should be disseminated to reinforce the importance of maintaining the confidentiality of these operations and the proper way to notify authorized individuals of armed personnel onboard the aircraft.