Its not really anything exciting.
So originally the utility helicopter designation was HU-1 Iroquois (eventually it was changed to UH-1 Iroquois in 1962). The crews and passengers would affectionately call them "
Huey's" when talking about them because of the HU designation. Eventually the name Huey stuck, to the point that the manufacturer Bell even put it on the pedals.
So despite official name of the UH-1 being the Iroquois, it is known by everyone and called by everyone the Huey.
View attachment 757192
Source of picture:
Bell Huey Helicopter US AirCraft Pedals Set For Model 204B 1967(Ser#204-001-702)