Neither is authentic. No one in 51 B.C. could have foreseen the existence of Jesus of Nazareth, much less that he would arrive in exactly 51 years. And George would not have been called George I until it became necessary to distinguish him from George II (“Victoria” will not become “Victoria I” until we have a “Victoria II”).
02/27/2024 UPDATE: Reader Emilio Díaz notes that King Juan Carlos I of Spain opted for a regnal number though no distinction was necessary. A joke runs Hoy voy a ver a Juan Carlos primero, y a la reina después (“Today I’m going to see Juan Carlos first, and the queen later”). The practice varies among monarchies. (Thanks, Emilio.)