From Old Turkicotag, from Old Turkicōta- ("make a fire, to give out smoke, to fume"). Closely related to the shamanistic feature of a shaman (summoning different kinds of spirits or demons). See oda. Or from Sogdianʾwtʾʾk(ōtāk, “place, region”). Compare Azeri otaq, Turkish otağ, and Turkmen otag.