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Your business name really only has to be unique within the jurisdiction where it is registered -- so when you register the business with your state or county, a name search will be required. The procedure for that varies by county and state. You can easily do it yourself in some places, but not in others.

Once you create and register the business, if you wish to exclusively use a name, phrase, symbol, or design (or a combination of those) to identify and distinguish your business from anyone else's, you need to file a trademark application. For details, visit:
http://www.uspto.gov/main/trademarks.htm

Hope this helps. Best wishes.