Pepsi-Cola was first made in New Bern, North Carolina in the United States in the early 1890s by pharmacist Caleb Bradham. On August 28, 1898 , "Brad's drink" was changed to "Pepsi-Cola" and later trademarked on June 16, 1903. There are several theories on the origin of the word "pepsi".
The only two discussed within the current PepsiCo website are the following: 1) Caleb Bradham bought the name "Pep Kola" from a local competitor and changed it to Pepsi-Cola. 2) "Pepsi-Cola" is an anagram for "Episcopal" - a large church across the street from Bradham's drugstore. There is a plaque at the site of the original drugstore documenting this while PepsiCo has refuted this theory.
Another theory is that Caleb Bradham and his customers simply thought the name sounded good or the fact that the drink had some kind of "pep" in it because it was a carbonated drink, they gave it the name "Pepsi".
As Pepsi was initially intended to cure stomach pains, many believe Bradham coined the name Pepsi from either the condition dyspepsia (stomachache or indigestion) or the possible one-time use of pepsin root as an ingredient (often used to treat upset stomachs). It was made of carbonated water, sugar, vanilla, rare oils, and kola nuts. Whether the original recipe included the enzyme pepsin is disputed
https://en.wikipedia.org/wiki/Pepsi