You can search copyrights in the US at the
Copyright.gov site.
What you are looking for likely more along the lines of a trademark, which can be searched (in the US) at the
USPTO site.
However, you will likely also want to check to see if anything has been incorporated already in your state. For example, you can search Texas via the
Comptroller's web site. (For an example, search Reliant Energy Inc or AceMiles)