This is the name given to a written decision by supreme court justices that, while they agree with the final outcome of the case, they do not agree with the reasoning behind the final outcome.

The name is "Concurring Opinion".

In law, a concurring opinion is in some legitimate frameworks a composed decision by at least one judges of a court which concurs with the choice made by most of the court, however states unique (or extra) reasons as the reason for his or her choice.