ONlwSG

bogha m. [ˈb̥o-ə], [ˈb̥o-o], gen. idem, ‘bow (archery, music etc.); bow, bend; arc, arch, vault; green bow-shaped area by river; crotch, fork, breech (human or animal); binding ring (in metal casting)’ (AFB^˄), 

Also ‘rainbow’, although this is more specifically bogha-frois(e), with genitive of SG fras ‘shower’.

Ir. idem and EG boġa are probably from ON boga (with a medial fricative), accusative of bogi m. ‘bow (rainbow; arch; weapon)’ (NO), 

Most authorities cite ON bogi nom.: (Early Gaelic) Bugge (1912, 298); Craigie (1894, 160); Marstrander (1915a, 22, 59, 64, 100, 112; de Vries (1962, 47); Schulze-Thulin (1996, 104); eDIL^˄; (Irish) Bugge (ibid.); Craigie (ibid.); Sandberg-McGowan (1996, 226); (Scottish Gaelic) Craigie (ibid.); Oftedal (1983, 155: boga acc.); Cox (1991, 492: boga acc.). McDonald (2009, 343) cites both bogi and boga.

although OEng. boga m. would be expected to yield the same result, 

So MacBain (1911) and MacLennan (1925).

and it is likely that the original senses of SG bogha have been reinforced on the one hand and supplemented on the other over time from Scots and/or English bow. Indeed, for Easter Ross, Watson (2022, 124, s.v. bogh’) records SG /bɤu̯/ ‘(rain)bow’, which is presumably a loan from Scots /bʌu/ ‘bow’.