Preheat the oven to 375 degrees F.
Bring a large pot of water to a boil and cook the macaroni; drain well.
Combine the squash, milk, broth and garlic in a medium saucepan and bring to a boil over medium-high heat. Reduce the heat to medium and simmer until the squash is tender when pierced with a fork, about 25 minutes.
Put the hot squash mixture in a blender and add the Greek yogurt, salt and pepper. Replace the blender lid with a clean towel (to let steam escape without the mess) and blend until smooth.
Put the squash mixture in a bowl and stir in the Gruyere, Romano, 1/2 cup of the Cheddar and 1/2 cup of the mozzarella until combined. Add the macaroni to the squash mixture, and stir until combined. Spread the mixture evenly in a 13-by-9-inch glass or ceramic baking dish and sprinkle the top with the remaining 1/2 cup Cheddar and 1/2 cup mozzarella.
Bake until bubbly, about 20 minutes.