In Plautus's play Amphitryon, Sosia is Amphitryon's slave. At one point in the play, the god Mercury disguises himself as Sosia and when the real Sosia appears, the god beats him up and sends him packing. The poor guy is totally baffled from being accosted by his own doppelgänger. If I understand correctly, this scene has led, in Italian and Spanish, to the name "Sosia" becoming a byword for someone's double.
It's interesting that the Roman theater has had so little impact on English.