What is a wall called which has plywood installed behind the drywall?
I don't know that there's a name for the wall as a whole. The sheathing is something I'd simply  refer to as "backing", as in "this wall has integrated support backing". It's also commonly done with lumber fit between studs as needed.

There are walls with integrated plywood that are part of the structural design. They're known as "shear walls" and they provide diagonal rigidity, often in earthquake or hurricane zones or in larger buildings. That's not what we're talking about here, though.