For all its life Pepsi has struggled to make itself distinct from Coke. For a while it simply gave you more - bigger bottles for the same price.

They never played up the Pepsin angle as much as you'd expect. It was just one of those things they either figured you knew (pepsin! It's good for digestion) or the vogue for things pepsin had passed, and it was too much trouble to change the name.

Wikipedia:

On three separate occasions between 1922 and 1933, The Coca-Cola Company was offered the opportunity to purchase the Pepsi-Cola company, and it declined on each occasion.

Imagine how the world would be different today.