Sorry, but that is not correct. You are the next person. You are the next customer. You don't put an article in front of an adjective.
Actually, in "you are the next", "next" is functioning as a pronoun replacing "next one", rather than an adjective, and thus is correct with "the". In fact, the Cambridge Dictionary specifically says, "We can use next as a pronoun with or without the".
Look, I have been speaking American English for 27 year, and I have lived all over the country and no one says, "the next." If you want to sound like a stuffy, old dictionary, then that's fine. If you want to speak like a native, then simply say, "next."