I prefer "Allen" over "hex" because it is more descriptive. If I want to refer to an "allen head" bolt, anybody knows I mean a bolt woth a round head and a hex shaped recessed (or female) opening. If I used "hex head", half might take it as the allen head I meant, and half might take it to mean a bolt with a hex-shaped head (the kind you use an ordinary socket on).
There doesn't seem to be a good record of who invented the "allen key", but some sources say it was G.F. Heublein and Brothers in Hartford, CT who supposedly also gave us the Graham Cracker and the first pre-mixed cocktail, all in the late 1880's. Just like there was the "Crescent Company" who made adjustable wrenches which caused most of us to call any adjustable wrench a "cresent wrench", I always assumed there was an "allen tool company" who made the first widely used "hex keys"....well, if there was I can't find it.
Anyhow, whether it's keys, wrenches, ratchet-driven sockets or screwdrivers....if they have a 6 sided male tip on them, I call them Allen.