Can a business owner post your full name and your photograph, with an amount of money they say you owe them, on the wall of their business? Does it violate any right to privacy?
Assume for the sake of argument that, unlike in this question, the statement is true.
That is going to depend very much on the the jurisdiction, and on the specific facts. If the statement that the pictured person owes a debt is false, this may be a case of defamation, but that was explored thoroughly in Can you post a picture in your business to embarrass or defame a customer? and its answers.
See FindLaw's page "What Is Invasion of Privacy?" for an overview of the classic privacy torts. See also this page quoting the Restatement (2nd) of Torts, § 652 See further the Wikipedia article "Privacy laws of the United States" which gives a history of the four torts.
Note that not all US states recognize all, or indeed any, of the privacy torts. Nor do all non-US jurisdictions. In some places these torts have been recognized, or blocked, by legislation, in others by court decision. And in the US they are limited by the federal First Amendment's guarantee of freedom of speech.
There is, in general, no right to privacy in one's physical appearance under any of the standard privacy torts, except that if one's likeness is being used to advertise something, or imply sponsorship or approval of a commercial product, many jurisdictions protect a right of publicity (sometimes called the tort of Appropriation of Name or Likeness). But here it does not appear that the image is being used to advertise or promote or sponsor anything, so that would not apply.
The tort of Intrusion upon Solitude and Seclusion would only apply if the picture were taken on someone's private premises or somewhere else there the person had a reasonable expectation of privacy. Otherwise it would not apply, there is no general right to privacy for a picture taken in public.
The tort of Public Disclosure of Private Facts could possibly apply if the fact of the unpaid debt had been carefully kept secret, and if its disclosure would be highly offensie to a reasonable person. But nothing that is a matter of public record can be the subject of such a suit anywhere in the US, because under Cox Broadcasting Corp. v. Cohn, 420 U.S. 469 (1975) publication of facts derived from public records is protected under the first and fourteenth amendments, even against a specific state law granting protection. This will obviously not apply outside the US.
If the statement of the debt were true, but in some significant way misleading, the tort of False Light might apply. This is described by the Restatement of Torts (2nd) § 652E as:
One who gives publicity to a matter concerning another before the public in a false light is subject to liability to the other for invasion of privacy, if (a) the false light in which the other was placed would be highly offensive to a reasonable person, and (b) the actor had knowledge of or acted in a reckless disregard as to the falsity of the publicized matter and the false light in which the other would be placed.
Note that the standard of (b) above is the same as the "Actual Malice" standard for defamation cases where the plaintiff is a public figure. False light cases are in many ways similer to defamation cases, and some jurisdictions have treated themn as identical tro defamation, while otrhrs do not recognize them at all. Nothing in the facts stated in the question would imply a false light claim, but more context might possibly support such a claim,.
Nothing in the question clearly indicates that any privacy-based tort would apply, but the facts are stated it a very brief way in the question. Further context and detail might clarify the answer one way or the other.
This answer is largely based onunited-states law, althoguh some of it will apply elsewhere.
In the EU this would be already illegal without the debt.
The lack of consent is implied in the question, and no other GDPR exception ground applies.
