Filing for a trademark registration puts the world on notice that you intend to use and protect your name. And if you are awarded a trademark registration by the US Patent and Trademark Office, you will have powerful tools to prevent use of that name by anyone else for similar goods or services throughout the United States.
If you file for and manage to get an EU trademark (European Community trademark, also called a CTM), you will have protection for your name throughout the 27 European Union countries.
And through international trademark treaties, these registrations can be used to claim priority (date of first use) elsewhere.
Also, under the Uniform Domain Name Dispute Resolution Policy agreement, if a cybersquatter has registered URLs that are the same or deceptively similar to your name, it is easier and quicker for you to dispute this if your name has been registered as a trademark.