The Town of Addison was originally named "Noell Junction" in honor of S. S. Noell. However, when a post office was authorized it was discovered there was already a post office designated as "Noel" in another part of Texas. In 1904 the town was then renamed for local carpenter and Civil War veteran Addison Robertson.

Addison served as the second postmaster from 1908 to 1916. Civic-minded even at the age of seventy-nine, Addison also served as an undercover Secret Service agent during World War I and helped with the capture of rebels in Wichita Fallas who were smuggling guns and planning to overthrow the government.