Mary, as the mother of Jesus, would not have had the surname "Christ" before Jesus was born. "Christ" is a title derived from the Greek word "Christos," meaning "anointed one," which is a translation of the Hebrew word "Messiah." It's a title that signifies Jesus' role and identity, not a family surname.
Mary would have been known as Mary of Nazareth, or simply Mary, daughter of [her father's name]. Surnames weren't commonly used in the way we understand them today in that time and place. People were usually identified by their given name, their father's name, and/or their place of origin.