Etymology
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Words related to william

will (n.)
Old English will, willa "mind, determination, purpose; desire, wish, request; joy, delight," from Proto-Germanic *wiljon- (source also of Old Saxon willio, Old Norse vili, Old Frisian willa, Dutch wil, Old High German willio, German Wille, Gothic wilja "will"), related to *willan "to wish" (see will (v.1)). The meaning "written document expressing a person's wishes about disposition of property after death" is first recorded late 14c.
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*kel- (1)

Proto-Indo-European root meaning "to cover, conceal, save."

It forms all or part of: Anselm; apocalypse; Brussels; caliology; Calypso; calyx; ceiling; cell; cellar; cellular; cellulite; cellulitis; cilia; clandestine; cojones; coleoptera; color; conceal; eucalyptus; hall; hell; helm (n.2) "a helmet;" helmet; hold (n.2) "space in a ship below the lower deck;" hole; hollow; holster; housing (n.2) "ornamental covering;" hull (n.1) "seed covering;" kil-; kleptomania; occult; rathskeller; supercilious; Valhalla; William.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit cala "hut, house, hall;" Greek kalia "hut, nest," kalyptein "to cover," koleon, koleos "sheath," kelyphos "shell, husk;" Latin cella "small room, store room, hut," celare "to hide, conceal," clam "secret," clepere "to steal, listen secretly to;" Old Irish cuile "cellar," celim "hide," Middle Irish cul "defense, shelter;" Gothic hulistr "covering," Old English heolstor "lurking-hole, cave, covering," Gothic huljan "to cover over," hulundi "hole," hilms "helmet," halja "hell," Old English hol "cave," holu "husk, pod;" Old Prussian au-klipts "hidden;" Old Church Slavonic poklopu "cover, wrapping."

helm (n.2)

"a helmet, a defensive cover for the head," from Old English helm "protection, covering; crown, helmet," from Proto-Germanic *helmaz "protective covering" (Cognates: Old Frisian, Old Saxon, Old High German helm, German Helm, Old Norse hjalmr, Gothic hilms), from PIE root *kel- (1) "to cover, conceal, save." Italian elmo, Spanish yelmo are from Germanic.

billy (n.)
"club," 1848, American English, originally burglars' slang for "crowbar;" meaning "policeman's club" first recorded 1856, probably from nickname of William, applied to various objects (compare jack, jimmy, jenny). But compare French bille "a short, stout stick" (see billet (n.1)). Billy-goat as a familiar name for a male goat is from 1826.
hillbilly (n.)

"southern Appalachian person," by 1892, from hill (n.) + Billy/Billie, popular or pet form of William. In reference to a type of U.S. folk music, first attested 1924.

I would hate to see some old railroad man come here and take my job, and then, I don't think it is right to hire some Hill Billy and give him the same right as I just because he was hired the same time I was. [The Railroad Trainmen's Journal, vol. ix, July 1892]
In short, a Hill-Billie is a free and untrammelled white citizen of Alabama, who lives in the hills, has no means to speak of, dresses as he can, talks as he pleases, drinks whiskey when he gets it, and fires of his revolver as the fancy takes him. [New York Journal, April 23, 1900]

In Scott's collection of Border ballads, billie is a frequent term of address or intimacy, "comrade, companion, a brother in arms," "a term expressive of affection and familiarity" also "a brother; a wooer of a woman," and generally "a young man" [Jamieson, 2nd edition]. It is said to be a variant of bully (n.) in its old sense of  "sweetheart," also "fine fellow."

Wilhelm 
German form of William (q.v.). Fem. form is Wilhelmina. Wilhelmine (adj.) is "pertaining to the reign of Wilhelm II," emperor of Germany 1888-1918. Berlin's Wilhelmstrasse was the pre-1945 headquarters of the German foreign office, hence used metonymically for "German foreign policy" (compare Quai d'Orsay).