Gouge
late Middle English: from Old French, from late Latin gubia, gulbia, perhaps of Celtic origin; compare with Old Irish gulba ‘beak’ and Welsh gylf ‘beak, pointed instrument’.
wiktionary
From Middle English gouge(“chisel with concave blade; gouge”), from Old French gouge, goi(“gouge”), from Late Latin goia, [1] gubia, gulbia(“chisel; piercer”), borrowed from Gaulish *gulbiā, from Proto-Celtic *gulbā, *gulbi, *gulbīnos(“beak, bill”). The English word is cognate with Italian gorbia, gubbia(“ferrule”), Old Breton golb, Old Irish gulba(“beak”), Portuguese goiva, Scottish Gaelic gilb(“chisel”), Spanish gubia(“chisel, gouge”), Welsh gylf(“beak; pointed instrument”), gylyf(“sickle”). [2]
The verb is derived from the noun. [3]
etymonline
gouge (n.)
mid-14c., "chisel with a concave blade," from Old French gouge "a gouge" (14c.), from Late Latin gubia, alteration of gulbia "hollow beveled chisel," probably from Gaulish (compare Old Irish gulban "prick, prickle," Welsh gylfin "beak"). Meaning "an imposition, a cheat" is from 1845, American English colloquial.
gouge (v.)
1560s, "to cut with a gouge," from gouge (n.). Meaning "to force out with a gouge" (especially of the eyes, in fighting) attested by 1800. Meaning "to swindle" is American English colloquial from 1826 (implied in plural noun gougers). Related: Gouged; gouging.