karenessex,
I know exactly the type of headset you are referring to. Many years ago they were issued to us as standard for doing aircraft push-backs, ground runs etc. I don't recall there being any particular technical term for them and although its quite possible they were used in other industries they seemed to be in pretty widespread use by many airlines. Manufacturers name escapes me too.
You might have trouble tracking one down now as they have been replaced by a more modern looking headset with a boom mike instead of the handheld mouthpiece. The new ones are much lighter for the wearer, easier and cheaper to repair and you don't have the potential danger of the mouthpiece dangling around tugs, towbars, moving aircraft parts etc. One advantage they did have however was that with the mouthpiece pressed to the face there was very little background noise introduced when communicating with the flight deck giving much clearer comms.