For much of American history, name changes did not require court action. A person could simply start using a new name–as long as they weren’t going to engage in any fraudulent activity. Your ancestor in 1880 could simply have chosen to use a new name when he or she moved into a new town.
Sometimes immigrants would take a new name when they naturalized. That name may have been based on the name they had in their native language, but there was no law that they had to literally translate.
Comprehensively searching your ancestor may help reveal name changes as land records, estate records, other court records, military pension materials and other records may document the name change.
Good ol’ Riley was originally named Latte when he came home from the shelter and we named him Riley. It was a complete coincidence (seriously) that I have a great-great-grandfather with the same name. Sometimes coincidences happen as well.
Obviously a dog in 2014 didn’t need to officially have his name changed. There’s a good chance your ancestor in 1814 didn’t need any official paperwork to change his name either.