[...] the word was-a, gen. wasan (masc.), satyrus, faunus, a sort of genius of the woods, also wudewasa, faunus sylvaticus. This word is allied to the clearly formed word wasjan, insanire, furere, bacchari; also to the Old Norse vasa, licentius incidere; vas (neut.), licentior incisus, animosior progressus. [...]

Leo, Heinrich, Treatise on the Local Nomenclature of the Anglo-Saxons,
London: Edward Lumley, 1852, p. 100.

[...] Wassing is derived from wasa, faunus, and is patronymic—the descendant of a vasa. Examples: [...] Wassingatún, [...].

Leo, Heinrich, Treatise on the Local Nomenclature of the Anglo-Saxons,
London: Edward Lumley, 1852, pp. 101.

TU’N, es ; m. [...]   1. A place fenced round or enclosed; [...]   3. A place of residence, house, dwelling, village, TOWN, a territory lying within the bounds of a town; [...]

Bosworth, Joseph, A Dictionary of the Anglo-Saxon Language, London: Longman, Rees, Orme, Brown, Green, and Longman; Talboys, Oxford; Stevenson, Cambridge, 1838, p. 401, col. 78y.

The derivation of Washington...

Washington = Anglo-Saxon, Wassingatu'n
      = Wassing + tu'n
      = "descendant of a wasa/vasa" + tu'n
      = "descendant of a wasa/vasa" + "town"
      = "the town of the descendants of the wasa/vasa"
      = "the town of the descendants of the faun, satyr, etc."