How do I protect my new company name?

Edit [Moderator]: Moved from Legal to Business & Marketing.

I want to start a new, small company. I plan to go to the records office in my county to register an assumed name for the business. I have 2 questions. I can search their database to make sure the name I want is not taken in my county, but is there a larger database somewhere so I can see if the name has been registered somewhere else? Also, is there a way I can register my name for a larger area than my county so people elsewhere will see the company name has been registered here? My guess is that I will just need to trademark the name when I begin using it. Thanks for any feedback.