Is there a name for the area for aircraft to back track near the runway threshold?
It sounds like you're talking about these:



I'm not sure if the designation is "official", but pilots in the US (and the FAA in various documents) usually refer to such areas as a "Runway Turnaround Area" or simply "Runway Turnaround".
Their purpose is to allow aircraft which have back-taxied on the runway (or landed and rolled past the taxiway turn-offs) to turn around to position for take-off or return to a taxiway turn-off.



Note that the "runway turnaround" is distinct from a "run-up area": The runway turnaround is considered to be part of the runway, so an aircraft occupying that area is occupying the runway. A run-up area is generally a distinct area, usually off a taxiway, where aircraft can perform engine run-ups prior to entering the runway.