Regarding that, I have an interesting vintage piece from 1971 which may help explain how the "barber's" aka "babar's" qualifier entered into the picture. As legend has it, the king of the elephants had a razorburn problem. In order to solve this, babar's barber introduced him to the straight razor. As you can probably guess, his schnozz was always in the way. So Barb, Babar's Barber, suggested Babar let the Barber create a special design just for him in mind. Borrowing from what was soon to become known as the barber's notch, babar's barber barb and her brother-in-law bob the steel worker came up with a design which allowed for the passage of the razor around babar's prominent snout. See for yourself:
Attachment 77231
So the "Barber" in "Barber's Notch" is actually "Babar". If anything, hollow point razors with larger than average notches should be referred to as having a "Babar's Notch"