Either you want to have a dominant cheese taste (like a cheeseburger), or it's an ingredient that works well with many other ingredients.
The important thing is to use a good cheese, with a good taste, and if you want it to melt, to follow a little trick.
But to make a long story short, there are 3 really essential points:
1) Try to avoid, if possible, the so-called "hamburger cheese", fluorescent orange squares, soft and flat, in plastic, with an implausible composition for what is supposed to be cheese, and which contains actually very little cheese. It's tempting to buy it because it melts quickly, but it's not really top notch.
2) And then, go for real good cheese instead. Soft cheeses like Morbier, Saint-nectaire, Mozzarella, raclette, Camembert, or others, which you cut into thin slices as possible (yes, it's not easy), work by themselves.
Note however that other firmer cheeses are also possible, I'm thinking in particular of Comté (my favorite) or Cheddar, both old, cut into thin strips with a peeler or grated coarsely, they don't melt as much, but bring a rather top taste to the burger.
3) That's really the trick: When you're cooking the steaks on the second side, you've just flipped them over, put the cheese strips directly on top of the steaks in the pan/plancha while they're cooking, you can even cover the pan to make it easier to melt, or cover the burger with a bowl, and leave it on standby like that, in the warmth, before assembling your burger.
When ready to assemble, remove the steak + melted cheese with a spatula and place them on the bun before continuing with the other ingredients.
In summary: Real good cheese if possible, and put on the meat at the end of cooking still in the pan, possibly covered, to facilitate its melting.
