What is it called when a submarine goes sonar quiet.?

The Navy term is "Silent Running"; when ordered, a submarine crew refers to one of the battlestations rigging bills to "Rig for Silent Running". It tells the crew which systems to shut down or reduce operations on, and all non-essential personnel not on watch or at critical tracking stations are ordered to their racks.

The usage hails from the Fleet Submarine days, when detectable noise was a real issue when dealing with attacking Destroyers of the day. Limited speed, maneuverability, and depth capability required every advantage to avoid detection, and Silent Running was part of that strategy.

Today's modern submarines are quiet enough that they are difficult to detect by anything other than another submarine, and even that's not easy with today's improved Sonar systems. However, being too quiet is also a dead giveaway in the ambient noise of the ocean; a trained Sonar crew will notice an acoustic dead spot moving through the water as well.

The ability to use the ocean environment to its advantage (depth, thermoclines) to hide in acoustic areas of advantage has also made the need for SR almost obsolete.