There are many Japanese chefs that use foods of Western origin to create original dishes, and I'm sure cheese is no exception.
Personally, I think mozarella is most versatile to use with Japanese cooking because it's mild in taste. I think it can be used very much like tofu, though it may differ in style of preparation because of the difference in texture.
Cheese of stronger scents and flavors can also be used. But, you'll have to learn from the top chefs. Maybe, you'll find clues searching the Web for top Japanese restaurants and chefs around the world.