The name Reading is a boy's name of English origin meaning "son of the red-haired". Reading and is often added to user-created lists like Puritan Surnames and discussed in our forums with posts like "New: Movie Title Family Name Game!".
From the experts:
Inventive way to honor a redheaded ancestor, though most people would mispronounce it reeding, making it sound to some kids like a school assignment: Redding is a preferable spelling.