Cook the pasta according to the package directions. Reserve 1 cup of the cooking water, drain the pasta, and return it to the pot.
Heat the oil in a medium skillet over medium-high heat. Add the zucchini, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook, stirring, until the zucchini is tender and any liquid has evaporated, about 5 minutes. Stir in the garlic and cook 1 minute more. Add all but 2 tablespoons of the cheese to the pasta. Add the reserved pasta water, 3/4 teaspoon salt, and 1/4 teaspoon pepper. Stir until creamy.
Serve the pasta topped with the zucchini, lemon zest, and the remaining cheese.
Tip: Fresh goat cheese is creamy and soft, which makes it ideal for incorporating into pasta dishes. Buy a log and crumble your own; the precrumbled bits sold in stores often don't melt as well, and they can be more expensive.