Ambulance was used at first to separate from others, but maybe not so useful indeed. The Four-Door Sedan was used in descriptive name of some cars, no? Especially on older cars.
Even for recent ones, like the Citroën C4, in its hatchback version is officially named "berline" (means "sedan") to differentiate it from the coupé, though that it is not in the model name, so just put as extra info.
For those which did not use it in official brochures etc., it should not be mentioned.