Copyright registration is meaningless in this context. It is for the registration of complete works, mainly to prove their existence at a certain time.
Trademark registration (USPTO) could be relevant to this situation, but it depends from the specific classes of goods and services the trademark is registered for.
There is nothing that prevents you from registering a domain name if it is still available, or from buying a domain from someone else. The copyright registration is not relevant. The trademark registration could be for other classes or you might reside in a country for which the trademark registration is not relevant.
I am not a lawyer, this is not legal advice.