The word "denomination" comes from the French word now spelled almost exactly the same and meaning exactly the same thing as in English. However when it was loaned to English hundreds of years ago the word simply meant naming something. This is still a lesser-used, action noun form of the word. If you denominate your pet cat "Leo", that is your denomination of him.
The French word in turn comes from the Latin word dēnōminātiō, meaning a metonymy. A metonymy is when something is called something descriptive but as a proper name, not as a description. The White House is a white house, but that is its name, not a a description. The idea carried across is giving something a new, "improper" name.
Few denominations chose their own names. Most were simply called something descriptive because of their practices or history which then stuck:
- Lutherans were the followers of Martin Luther.
- Calvinists were the followers of John Calvin.
- Methodists were so named because of their extremely orderly meetings.
- Anabaptists, meaning "those who baptize again", were Christians who believed baptism should happen after salvation, so they baptized believers who had previously been baptized as children.
- Presbyterians were governed by presbyters (derived from the Greek πρεσβῠ́τερος, meaning an elder).
- Mormons followed the Book of Mormon.
These groups were given new names—denominations.