Variant of Emery, or a name for someone from Emborough or any of the places called Hembry. Emborough comes from Old English emn "flat-topped" and beorg "mound, hill". Henbury in Gloucestershire comes from Old English hēah "high" and burh, byrig "fortified place". Henbury in Chesire comes from Old English hæmed "community" and burh, byrig "fortified place".