“Magot” literally means “stocky figurine from the Far East”. The name originally belonged to a fabric and novelty shop at nearby 23 Rue de Buci. The shop sold silk lingerie and took its name from a popular play of the moment (19th century) entitled Les Deux Magots de la Chine. Its two statues represent Chinese “mandarins”, or “magicians” (or “alchemists”), who gaze out over the room.
It’s such a famous place that it has its own Wikipedia page. About the name, it says: