What is that thing pan cover called you put over a hamburger on flat top grill to melt the cheese?

The thing you put over a hamburger on a flat top grill to melt the cheese is called a cheese melter or a cheese press. It's usually a metal dome with a handle that fits over the burger.

Some people also use a burger press to help melt the cheese. This is a flat metal press that weighs down the burger and cheese, promoting even melting.