The description below is of a process that occurs roughly in the manner suggested but is not generally known by that name in any body of law commonly used in the United States.
Generally, allocute means "to speak out formally." In the field of apologetics, allocution is generally done in defense of belief. In politics one may allocute before a legislative body in an effort to influence their position on an issue. In law, it is generally meant to state specifically and in detail what one did and/or why, often in relation to commission of a crime.
In most jurisdictions, a defendant is allowed the opportunity to allocute - that is, explain himself, before sentence is passed. Some jurisdictions hold this as an abolute right, and in its absence, a sentence may potentially be overturned, with the result that a new sentencing hearing must be held.
Allocution is sometimes required of a defendant who pleads guilty to a crime in a plea bargain in exchange for a reduced sentence. In this instance, allocution can serve to provide closure for victims or their families, and it nearly always removes any doubt as to the exact nature of the defendant's guilt in the matter.