I am not sure what exactly you are asking, as your question is not complete and you offered no additional detail.
But, what I think you are asking: Do you need to file a trademark for a domain name.
In the US, the answer is no. You *can* apply for a trademark for your brand name which may also be your domain name. But a trademark is not required for a domain.
On the flip side, if someone owns the trademark to the word/words of your domain, they may pursue legal options to prevent you from using said domain name.
All the best,