What callsign would a medical emergency flight use?
The variety of callsigns used for medical flights are covered in the AIM 4-2-4:


  b. Air Ambulance Flights.
  
  Because of the priority afforded air ambulance flights in the ATC system, extreme discretion is necessary when using the term “MEDEVAC.” It is only intended for those missions of an urgent medical nature and to be utilized only for that portion of the flight requiring expeditious handling. When requested by the pilot, necessary notification to expedite ground handling of patients, etc., is provided by ATC; however, when possible, this information should be passed in advance through non−ATC communications systems.
  
  
  Civilian air ambulance flights responding to
  medical emergencies (first call to an accident scene,
  carrying patients, organ donors, organs, or other
  urgently needed lifesaving medical material) will be
  expedited by ATC when necessary. When expeditious
  handling is necessary, include the word
  “MEDEVAC” in the flight plan per paragraphs 5−1−8
  and 5−1−9. In radio communications, use the call
  sign“MEDEVAC,” followed by the aircraft registration
  letters/numbers.
  EXAMPLE− MEDEVAC Two Six Four Six.
  Similar provisions have been made for the use
  of “AIR EVAC” and “HOSP” by air ambulance
  flights, except that these flights will receive priority
  handling only when specifically requested.
  Air carrier and air taxi flights responding to
  medical emergencies will also be expedited by ATC
  when necessary. The nature of these medical
  emergency flights usually concerns the transportation
  of urgently needed lifesaving medical materials
  or vital organs. IT IS IMPERATIVE THAT THE
  COMPANY/PILOT DETERMINE, BY THE
  NATURE/URGENCY OF THE SPECIFIC
  MEDICAL CARGO, IF PRIORITY ATC ASSISTANCE
  IS REQUIRED. Pilots must include the word
  “MEDEVAC” in the flight plan per paragraphs 5−1−8
  and 5−1−9, and use the call sign “MEDEVAC,”
  followed by the company name and flight number for
  all transmissions when expeditious handling is
  required. It is important for ATC to be aware of
  “MEDEVAC” status, and it is the pilot’s responsibility
  to ensure that this information is provided to ATC.
  EXAMPLE−
  MEDEVAC Delta Thirty−Seven.