The name of the Swiss cheese that has a nutty flavor and is often used in fondue is called "Gruyere" cheese. It is a hard cheese that originates from the town of Gruyere in Switzerland and is made using unpasteurized cow's milk. It has a distinct flavor and aroma, making it a popular choice for not only fondue but also sandwiches, salads, and casseroles. Gruyere cheese is often aged for 6-12 months, which contributes to its nutty taste and complexity.