Greek Meaning: The name Natasha is a Greek baby name. In Greek the meaning of the name Natasha is: Born at Christmas. Russian Meaning: The name Natasha is a Russian baby name. In Russian the meaning of the name Natasha is: Born at Christmas.American Meaning: The name Natasha is an American baby name.In American the meaning of the name Natasha is: Born at Christmas. Latin Meaning: The name Natasha is a Latin baby name. In Latin the meaning of the name Natasha is: Bom at Christmas.SoulUrge Number: 3. Expression Number: 1. People with this name have a deep inner desire to create and express themselves, often in public speaking, acting, writing or singing.he name Natasha is an American baby name. In American the meaning of the name Natasha is: Born at Christmas. Latin Meaning: The name Natasha is a Latin baby name. In Latin the meaning of the name Natasha is: Bom at Christmas.