Brad's Drink
I have a historical trademark book in my office with some additional info... "Brad" is because it was invented and sold by a pharmacist named Caleb D Bradham, before he branded it later as Pepsi Cola. He did really well with it until WW1 when there was sugar rationing and then sugar price fluctuations later. He lost ownership at a specific point when he bought sugar at a high and suddenly had to sell it way low in 1920.
On the other hand, I'd bet the designs from 1991-onward are the result of marketing executives doing a rebranding purely to pad out their resumes while they hustle on to their next promotion.