Haw
Old English haga, of Germanic origin; probably related to hedge (compare with Dutch haag ‘hedge’).
wiktionary
Imitative
From Middle English hawe, from Old English haga(“enclosure, hedge”), from Proto-Germanic *hagô (compare West Frisian haach, Dutch haag, German Hag(“hedged farmland”), Norwegian Bokmål hage(“garden”)), from Proto-Indo-European *kagʰom (compare Welsh cae(“hedge”), Latin caulae(“sheepfold, enclosure”), cohum(“strap between plowbeam and yoke”), Russian кош(koš, “tent”), коша́ра(košára, “sheepfold”), Sanskrit कक्ष(kakṣa, “curtain wall”)), from *kagʰ- 'to catch, grasp' (compare Welsh cau(“to clasp”), Oscan kahad(“may he seize”), Albanian kam, ke(“to have, hold”)).
Unknown.
Uncertain.
etymonline
haw (n.)
"enclosure," Old English haga "enclosure, fortified enclosure; hedge," from Proto-Germanic *hag- (source also of Old Norse hagi, Old Saxon hago, German Hag "hedge;" Middle Dutch hage, Dutch haag, as in the city name The Hague), from PIE root *kagh- "to catch seize; wickerwork fence" (see hedge (n.), and compare hag). Meaning "fruit of the hawthorn bush" (Old English) is perhaps short for *hægberie.
haw (v.)
"hesitate in speech," 1580s, imitative. Related: Hawed; hawing. The noun in this sense is from c. 1600. Haw-haw in reference to a style of affected upper class British enunciation is from 1841, imitative.