The combined mark protects the combination as filed. Each dominant and distinctive element within it also receives some level of implicit protection, meaning a third party who copies only the name or only the logo may still infringe on the combined mark registration, provided that element is sufficiently distinctive on its own.
What most trademark owners miss is that this implicit protection is narrower than what a dedicated wordmark or figurative mark registration would provide. A standalone wordmark gives you clear and unambiguous rights over the brand name in any form, but a figurative mark doesn’t do that. For clear, independent protection of each element, separate registrations are the stronger approach.