The point of a word is to convey meaning with a short string of sounds. The meaning of a word referring to a dish would normally describe the taste of the dish and what it's made of in general terms, because as you've pointed out, recipes are subject to individual variation. To say that a restaurant should not serve a dish called "carbonara" made with French cheese to me sounds similar to saying that an Italian carpenter should not sell a mahogany table and call it "tavolo in legno", because they don't grow mahogany in Italy. Who cares where the ingredients come from if the dish tastes good?