An Etymological Dictionary of the German Language/Hag
Hag, m., ‘hedge, fence, enclosure,’ from MidHG. hac, hages, m., n., ‘thorn bushes, copse, fence, enclosed wood, park,’ OHG. hag, m., once as ‘urbs’ (comp. HG. Hagen, and names of places ending in -hag); Du. haag, f., ‘enclosure, hedge,’ AS. haga, m., E. haw, ‘enclosure, small garden’; OIc. hage, m., ‘pasture.’ Only in Goth. is a cognate word wanting; comp. Hain, Here, Hagen, and Hecke. The derivation is uncertain; it is at all events not connected with hauen, root haw; the meaning of ModHG. behagen is unsuitable.