Is the verb "swallow" related to the noun?
From the OED in relation to swallow (the bird):
swallow ▪ I.swallow, n.1 (ˈswɒləʊ) Forms: 1 s(u)ualu(u)ae, swealwe, swalowe, -uwe, -awe, 1, 4 swalewe, swalwe, swolwe, 4 swalugh, swalu, 4–6 swalow(e, 5 swalue, sualowe, 5–7 swallowe, 6– swallow. [Com. Teut. (not recorded for Gothic): OE. swealwe wk. fem. = OS. suala, MLG. swalewe, swalue, MDu. swâluwe, -ewe (Du. zwaluw), OHG. swalawa, swalwa (MHG. swal(e)we, G. schwalbe), ON. svala for *svǫlva (MSw., Sw. svala, Da. svale):—OTeut. *swalwōn-, the etymological meaning of which is disputed.
Continental Germanic dialects have also forms of other types: without w in the final syllable, e.g. MHG. swal, swale, MLG. swale, WFris. sweal, swel; with m-suffix, e.g. HG. (local) schwalm, schwalme, Flem. swaelem; forms with dim. suffix are widespread in LG. and Fris., e.g. MLG. swalike, swal(e)ke, LG. swaalke, Flem. swalcke (Kilian), EFris., NFris. swâlk, WFris. swealtsje, sweltsje.]
- a. A bird of the genus Hirundo, esp. H. rustica, a well-known migratory bird with long pointed wings and forked tail, having a swift curving flight and a twittering cry, building mud-nests on buildings, etc., and popularly regarded as a harbinger of summer (cf. c). a 700 Epinal Gloss. 498 Hirundo, sualuuae. c 950 Guthlac x. (1909) 143 Þa comon þær sæmninga in twa swalewan fleoᵹan, and hi..heora sang upahofon. c 1000 Sax. Leechd. II. 156 Ᵹenim swealwan, ᵹebærn..to ahsan. Ibid. III. 44 Ᵹenim swolwan nest. c 1320 Sir Tristr. 1366 A swalu ich herd sing. c 1374 Chaucer Troylus ii. 64 The swalwe Proigne, with a sorwful lay,..gan make hir weymentinge. 1398 Trevisa Barth. De P.R. xii. xxii. (Bodl. MS.) lf. 122 b/1 In making of nestes þe swalowe is moste sliȝe. a 1450 Knt. de la Tour lxxx. 102 The dunge of swalues fell into the eyen of this good man Tobie. a 1529 Skelton P. Sparowe 404 The chattrynge swallow. 1579 Spenser Sheph. Cal. Mar. 11 The Swallow peepes out of her nest. 1611 Shakes. Wint. T. iv. iv. 119 Daffadils, That come before the Swallow dares...
I suspect the reference to the Old Teutonic swalwōn- by the OED, and its comment that the etymological meaning 'is disputed' might be a reference to Kluge's 1891 'An Etymological Dictionary of The German Language'.
Kluge has this to say:
No certain explanation can be given of the primary form swalwôn, f.; perhaps it represents swalgwôn-, pre-Teutonic swalkuân, to which Greek ἅλκύων is also traced.
Noting that ἅλκύων is Greek for halcyon, or kingfisher. All of this leaves me better informed, but none the wiser. There's more to be told about the pre-Teutonic roots perhaps and the link with that Greek word.