American Meaning: The name Rodney is an American baby name. In American the meaning of the name Rodney is: Famous. English Meaning: The name Rodney is an English baby name. In English the meaning of the name Rodney is: Island of reeds. A place name in Somerset.nglish Meaning: The name Rodney is an English baby name. In English the meaning of the name Rodney is: Island of reeds. A place name in Somerset.