What's the law regarding having to identify yourself? Theoretically speaking: If one goes to an appointment not carrying any form of ID, and it turns out to be a sting operation, and he gets arrested, what if he refuses to identify himself to LE or gives the wrong name? Can they jail him until he speaks? What does the law say about having to identify yourself and the consequences? Theoretically speaking of course.
The law says you have to identify yourself. The police won't just let a suspect walk away because he refuses to identify himself. If it worked that way, criminals could avoid punishment simply by leaving their ID at home and refusing to cooperate.
What the police will do if you refuse depends on where you are and what got them interested in you in the first place. In many places refusing to identify yourself to an officer is a crime, and sometimes it will prove to be a more serious crime than the one which got the police involved in the first place. The U.S. Supreme Court ruled last year that such laws are legal and may be enforced even where there is no probable cause to believe the person committed a crime, as long as there is a legitimate reason for the police to want to interview him.
At the very least you could be arrested and thrown in the tank on a charge of Vagrancy.