Bring a large pot of lightly salted water to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes; drain.
Heat a large skillet over medium heat and add olive oil. Place anchovies in the hot oil, pressing with the back of a wooden spoon until anchovies are melted in the oil, 2 to 3 minutes. Add garlic, shallot, kosher salt, red pepper flakes, thyme, oregano, and basil; cook for 1 minute. Increase heat to medium-high and cook, stirring frequently, until onion and garlic start to soften, 3 to 4 minutes.
Pour wine over onion mixture and cook 1 to 2 minutes. Mix clams and their juice into onion mixture; cook and stir for 2 to 3 minutes. Stir tomatoes into clam mixture and cook until sauce is heated through, 2 to 3 minutes; season with salt and black pepper. Add linguine and 1/2 of the parsley to sauce and mix. Garnish with remaining parsley and lemon zest.