The name Anastasia is a Russian baby name. In Russian the meaning of the name Anastasia is: Reborn. American Meaning: The name Anastasia is an American baby name. In American the meaning of the name Anastasia is: Reborn.Greek Meaning: The name Anastasia is a Greek baby name. In Greek the meaning of the name Anastasia is: Resurrection. One who will be reborn. Famous bearer: 4th-century martyr St Anastasia.Anastasia, famous daughter of Tsar Nicholas lI, last emperor of Russia, who many believe survived the 1918 massacre of her family.he name Anastasia is a Russian baby name. In Russian the meaning of the name Anastasia is: Reborn. American Meaning: The name Anastasia is an American baby name. In American the meaning of the name Anastasia is: Reborn.