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* As an English and Scottish surname of Norman origin, from the name Engaine, based on Old French engaigne (“ingenuity”), from Latin ingenium. Sometimes confused with Ingham. * As a French surname, from the verb gagner (“to obtain, gain”).

From Middle English gayn, gain, gein (“profit, advantage”), from Old Norse gagn (“benefit, advantage, use”), from Proto-Germanic *gagną, *gaganą (“gain, profit", literally "return”), from Proto-Germanic *gagana (“back, against, in return”), a reduplication of Proto-Germanic *ga- (“with, together”), from Proto-Indo-European *ḱóm (“next to, at, with, along”). Cognate with Icelandic gagn (“gain, advantage, use”), Swedish gagn (“benefit, profit”), Danish gavn (“gain, profit, success”), Gothic 𐌲𐌰𐌲𐌴𐌹𐌲𐌰𐌽 (gageigan, “to gain, profit”), Old Norse gegn (“ready”), dialectal Swedish gen (“useful, noteful”), Latin cum (“with”); see gain-, again, against. Compare also Middle English gaynen, geinen (“to be of use, profit, avail”), Icelandic and Swedish gagna (“to avail, help”), Danish gavne (“to benefit”). The Middle English word was reinforced by Middle French gain (“gain, profit, advancement, cultivation”), from Old French gaaing, gaaigne, gaigne, a noun derivative of gaaignier, gaigner (“to till, earn, win”), from Frankish *waiþanōn (“to pasture, graze, hunt for food”), ultimately from Proto-Germanic *waiþiz, *waiþō, *waiþijō (“pasture, field, hunting ground”); compare Old High German weidōn, weidanōn (“to hunt, forage for food”) (Modern German Weide (“pasture”)), Old Norse veiða (“to catch, hunt”), Old English wǣþan (“to hunt, chase, pursue”). Related to wide.

From dialectal English gen, gin, short for again, agen (“against”); also Middle English gain, gayn, gein, ȝæn (“against”), from Old English gēan, geġn (“against”). More at against.

From Middle English gayn, gein, geyn (“straight, direct, short, fit, good”), from Old Norse gegn (“straight, direct, short, ready, serviceable, kindly”), from gegn (“opposite, against”, adverb) (whence gagna (“to go against, meet, suit, be meet”)); see above. Adverb from Middle English gayn, gayne (“fitly, quickly”), from the adjective.

Compare Welsh gan (“a mortise”).