I agree with the statement of eat it as you would like it. For me, I would prefer it without the cheese, but if you are going to add cheese I like phatch's suggestion of Asiago. Just don't do what they do here in Wisconsin and throw either cheddar or mozz on just about everything!!! (not that I've ever seen them throw it on scampi but they do throw it on numerous fish dishes that I would never expect cheese on)
"Scampi are tiny, lobster-like crustaceans with pale pink shells (also called langoustines). Italian cooks in the United States swapped shrimp for scampi, but kept both names. Thus the dish was born, along with inevitable variations."