ITLL(in three lines or less): Airplanes are required to broadcast license plate numbers. You can request a temp tag for privacy. Offer only valid for US destinations.
Though for high profile figures, it'll take about five minutes for an astute observer to figure out what the aircraft is calling itself now.
Also of note: All aircraft information associated with a PIA is exempt from FOIA requests.
New FAA feature - anonymous IDs for private aircraft.