Greek Meaning: 1  The name Phoebe is a Greek baby name. In Greek the meaning of the name Phoebe is: The shining one. 2  The name Phoebe is an American baby name. In American the meaning of the name Phoebe is: The shining one. 3  The name Phoebe is a Latin baby name. In Latin the meaning of the name Phoebe is: Daughter of Leda.