The name Rufus is a Biblical baby name. In Biblical the meaning of the name Rufus is: Red. American Meaning: The name Rufus is an American baby name.In American the meaning of the name Rufus is: Red.Latin Meaning: The name Rufus is a Latin baby name. In Latin the meaning of the name Rufus is: Red; red haired.he name Rufus is a Biblical baby name. In Biblical the meaning of the name Rufus is: Red. American Meaning: The name Rufus is an American baby name.