I have noticed many people from outside the US get hung up on grilled cheese. We just call it that for some reason and no one really thinks about it. If we stop to think, we know it is not grilled, and as far as I’m aware, it’s the only thing we call “grilled” that is not grilled. I think the reason we do not call it a toasted cheese sandwich, or cheese toastie, as I think I’ve heard in the UK, is that would imply the use of a toaster (a standalone appliance with electric heating elements inside slots just big enough for a single slice of bread). I suppose griddled cheese might be a more accurate name, but we are too far gone to make that change.