For me, it all started with Raven from Teen Titans... No chance after that, I'm afraid.
Assuming I wasn't trolled by a historian, the name goth for our post-modern mortality-celebrating Cure-listening well-dressed counter-culture comes from the Romans, not because the barbarians at the gates were wearing black lipstick, but because Romans were prone to call any counter-culture in Rome gothic.
Rome was sacked by Visigoths more than once, and rebuilt again. So gothic was a term of derision by conservatives who liked classical styles and not these new-fangled buildings that were erected when the old one burned down, or for that matter, these new-fangled liberal ideas the kids go on about. A prime example is Ogival architecture (tall spires and flying buttresses) called Gothic for being the new Roman style by those who longed for the pre-sack skyline.
We see similar effects with other regional groups. Bohemians (the absinthe-drinking free-loving artists) only started with migrating creatives from Bohemia inspiring a (goth-adjacent) counter-culture celebrated across Europe. Also the attribution of French stuff typically having to do with sex or cooking e.g. French post cards (NSFW pin-up women) or French fries (julienned potatoes) much of which doesn't originate from France, but might have gained popularity in Paris.
I sort of agree, but I think you might be simplifying over a couple of steps.
Goth, as we interpret it today, comes most directly from the term gothic literature. Dracula. Frankenstein. Edgar Allen Poe. 18th and 19th century dark romantic literature often with a touch of horror thrown in. The association there was to the gothic architecture - the old cathedrals and buildings - that acted as a characteristic backdrop for those kinds of stories. Think gargoyles and flying buttresses and such. The gothic term there does probably come from Renaissance writers who were referring to the old architectural styles as “barbaric” (or at least very primitive and outdated) compared to the new styles. And, being the Renaissance, was probably a deliberate callback to the Roman era meaning of the word, because they loved their classical revival shtick.
