Military flights use the nose numbers during some portions of flight. Cougar and Merlin fly nose #203.
Screenshot from about 9:40 in Top Gun.
From airport freak
Military flights often use more than one call-sign during a flight. Administrative call-signs are used with air traffic control facilities similar to those of commercial operators. e.g. Navy Alpha-Golf-Two-One, Reach-Three-One-Seven-Niner Two.
Tactical call-signs are used during tactical portions of a flight, and they often indicate the mission of the flight and/or an aircraft's position in a formation.
For example, Canadian Air Force 442 Rescue Squadron, based at Comox, British Columbia uses the call-sign "Snake 90x" depending on the tail number of the helicopter: 901, 902, etc. When tasked on a search and rescue (SAR) mission, however, the aircraft call-sign becomes "Rescue 90x".