The changing of the name does not have anything to do with what something is.
You could switch the meanings of the word man and woman, but that doesn't change what the person is.
Hot dogs are also what the piece of meat is called with synonyms being frankfurter and weiner and a lone piece of meat is also not a sandwich.
A sandwich also needs two slices of bread which a hot dog does not have. A sub is technically not a sandwich for the same reason that a burrito and a hot dog is not a sandwich. They use one piece of bread.