Celtic Meaning: The name Alan is a Celtic baby name. In Celtic the meaning of the name Alan is: Harmony, stone, or noble. Also fair, handsome. Originally a saint's name, it was reintroduced to Britain during the Norman Conquest, remained popular throughout the Middle Ages, and was revived in the 19th century.See also Allen.he name Alan is a Celtic baby name. In Celtic the meaning of the name Alan is: Harmony, stone, or noble. Also fair, handsome. Originally a saint's name, it was reintroduced to Britain during the Norman Conquest, remained popular throughout the Middle Ages, and was revived in the 19th century. See also Allen.