Choosing a business name for your website or blog involves understanding something about federal trademark law -- please see the Trademark for Business Naming section for details. For a helpful general guide to choosing a business name, see FindLaw's Picking a Winning Name for Your Business. TNW Entrepreneur also has an excellent article by Julian Shapiro on common pitfalls in selecting a name for an Internet-based business and ways to avoid them.
There are a number of ways to check the availability of a name, including doing a basic internet search, searching the list of "fictitious" or "assumed" business names at your local county clerk's office, searching your state's database of "fictitious" or "assumed" business names, and searching the federal trademark database at the U.S. Patent and Trademark Office (free of charge). For details on checking the availability of a business name, see FindLaw's Make Sure Your Proposed Business Name Is Available.
You may already have a domain name for your website or blog. If not, when choosing a business name you should consider whether there is an available domain name that would work well with the business name. You can search for and register domain names by visiting a domain name registrar such as Network Solutions, Register.com, or Go Daddy.