The actual technical name for such an aerial is a "Centre loaded whip", or at least it would be if the coil was actually a tuned element in the aerial system.
In the duty this aerial is expected to work, just as an AM/FM car radio aerial and not as a specialist dual band VHF/UHF radiating element, the coil serves no tuned purpose, it's just a blingy and technical looking method of slightly shortening to bit sticking up in the air.