Confidentiality in an off-market sale is not secrecy. It is control over what is released, to whom, and when.
Confidentiality in a business sale is often described as anonymity. That is the wrong idea, and it sets an expectation that cannot be met — at some point a buyer who is going to acquire the business will know exactly which business it is.
The useful definition is control. The business is not publicly identified. Information is released progressively rather than all at once. Buyers can be qualified before they are given anything that identifies the company, and an NDA can be in place before identifying information is released. The seller decides each step.
That sequencing is what protects the things owners actually worry about: staff hearing it second-hand, a key customer using it as leverage, a competitor learning the business is in play and deciding to compete harder rather than buy.
It also improves the quality of the conversation. A buyer who has agreed to terms of confidentiality before receiving detail has already demonstrated something about their intent.