1660s, "willful destroyer of what is beautiful or venerable," from Vandals, name of the Germanic tribe that sacked Rome in 455 under Genseric, from Latin Vandalus (plural Vandali), from the tribe's name for itself (Old English Wendlas), perhaps from Proto-Germanic *wandljaz "wanderer." The literal historical sense in English is recorded from 1550s.
There does not seem to be in the story of the capture of Rome by the Vandals any justification for the charge of willful and objectless destruction of public buildings which is implied in the word 'vandalism.' It is probable that this charge grew out of the fierce persecution which was carried on by [the Vandal king] Gaiseric and his son against the Catholic Christians, and which is the darkest stain on their characters. [Encyclopaedia Britannica, 13th ed., 1926]
Old English Gota (plural Gotan) "a member of the Germanic people who lived in Eastern Europe c.100 C.E.," from Late Latin Gothus (plural Gothi), from Greek Gothos (plural Gothoi), from Gothic *Gutos, which is preserved in Gothic gutþiuda "Gothic people," the first element cognate with Old Norse gotar "men" (the second meaning "people; see Dutch). "The sense 'men' is usually taken to be the secondary one, but as the etymology of the word is unknown, this is uncertain" [Gordon]. The unetymological -th- in the modern English word is from Late Latin.
They entered history in 3c. C.E. on the lower Danube and later invaded the Roman Empire and were converted to Arian Christianity. Used in sense of "rude or uncivilized person; savage despoiler" (1660s) in reference to their fifth-century sacking of Roman cities (compare vandal, and French gothique, still with a sense of "barbarous, rude, cruel"). In 19c., in reference to living persons, it meant "a Gothicist" (1812), that is, "an admirer of the Gothic style, especially in architecture." Modern use as an adjective in reference to a subculture style (typically with lower-case g-) is from 1986, short for Gothic in this sense.
By 1982, when the legendary Batcave club opened in London, the music press had begun to use the term gothic rock to describe the music and fandom around which a new postpunk subculture was forming. [Lauren M.E. Goodlad & Michael Bibby, "Goth: Undead Subculture," 2007]