Old English brand, brond "fire, flame, destruction by fire; firebrand, piece of burning wood, torch," and (poetic) "sword," from Proto-Germanic *brandaz "a burning" (source also of Old Norse brandr, Old High German brant, Old Frisian brond "firebrand; blade of a sword," German brand "fire"), from PIE root *gwher- "to heat, warm."
Meaning "iron instrument for branding" is from 1828. Meaning "mark made by a hot iron" (1550s), especially on a cask, etc., to identify the maker or quality of its contents, broadened by 1827 to marks made in other ways, then to "a particular make of goods" (1854). Brand-name is from 1889; brand-loyalty from 1961. Old French brand, brant, Italian brando "sword" are from Germanic (compare brandish).