What is the name of the maximum altitude at which a helicopter can fly?
Like with fixed wing aircraft, it is called the ceiling. Usually two ceilings are distinguished;


service ceiling, where the aircraft can still achieve a positive rate of climb of either 100 fpm (propeller) or 500 fpm (jet).
absolute ceiling, the theoretical altitude at which no positive rate of climb can be achieved. In other words: the maximum altitude at which the aircraft theoretically can fly under maximum engine power.