A great number of dead bodies are transported by airplanes everyday. How will pilots report to ATC they are transporting it/them?
In the US, pilots may use the term "FALLEN HERO" to indicate they are transporting remains of military servicemembers and ATC will attempt to provide priority handling in accordance with the 7110.65 2–1–4q. This is the last in a long line of operational priorities, indicating treat better than simply "first-come first-served" but below any other conflicting priority.
Civilian pilots may use the term "MEDEVAC" or the now-archaic "LIFEGUARD" to indicate a request for priority when on an active air ambulance mission (I believe the terms "AIR EVAC" and "HOSP" are used by the military). These flights are afforded very high priority, second only to aircraft in distress. The term may be used when carrying patients or when carrying time-sensitive supplies or equipment, for example a donated organ or medicines.
To my knowledge there is no phraseology used to inform ATC there is a dead body on board. If there was a need for ATC to know about it (for example, the body is unexpectedly dead and the flight will need to be met by medical personnel) the pilot would use plain English.