Old English mona, from Proto-Germanic *menon- (cf. Old Saxon and Old High German mano, Old Frisian mona, Old Norse mani, Danish maane, Dutch maan, German Mond, Gothic mena "moon"), from PIE *me(n)ses- "moon, month" (cf. Sanskrit masah "moon, month;" Avestan ma, Persian mah, Armenian mis "month;" Greek mene "moon," men "month;" Latin mensis "month;" Old Church Slavonic meseci, Lithuanian menesis "moon, month;" Old Irish mi, Welsh mis, Breton miz "month"), probably from root *me- "to measure," in reference to the moon's phases as the measure of time.
A masculine noun in Old English. In Greek, Italic, Celtic, Armenian the cognate words now mean only "month." Greek selene (Lesbian selanna) is from selas "light, brightness (of heavenly bodies)." Old Norse also had tungl "moon," ("replacing mani in prose" - Buck), evidently an older Germanic word for "heavenly body," cognate with Gothic tuggl, Old English tungol "heavenly body, constellation," of unknown origin or connection. Hence Old Norse tunglfylling "lunation," tunglœrr "lunatic" (adj.).
Extended 1665 to satellites of other planets. To shoot the moon "leave without paying rent" is British slang from c.1823; card-playing sense perhaps influenced by gambler's shoot the works (1922) "go for broke" in shooting dice. The moon race and the U.S. space program of the 1960s inspired a number of coinages, including, from those skeptical of the benefits to be gained, moondoggle (cf. boondoggle). The man in the moon is mentioned since early 14c.; he carries a bundle of thorn-twigs and is accompanied by a dog. Some Japanese, however, see a rice-cake-making rabbit in the moon.