Here's how I've brainstormed business names in the past (this works in the USA, adjust appropriately if you're in another country):
1. Think of the concept you want to get across - what is your business about, and what makes it unique or the best in its class?
2. Write down keywords associated with the concept. Brainstorm possible names based on the keywords and the concept.
3. Convert the names to domain names (you'll need one of those if you want an internet presence).
4. Google the name (say, Acme Spiffy Widgets). See what comes up. See if the domain name is in use (e.g., enter acmespiffywidgets.com in the browser). Make sure the *.net and *.com versions are available, too. A site where you can check domain name registration is:
Whois.net
You may need to try variations of the domain name to find one that's available (e.g., acme-spiffy-widgets.com, acme-widgets.com, spiffy-widgets.com, etc.)
5. Go to the Patent & Trademark Office site and search for your company name here (click on the Search link at the right side of the page):
USPTO
You'll notice variations on the name that have been registered, and sometimes a logo image is registered but not the name.
6. If you need to tweak your names, search for synonyms for your keywords and repeat 1-6 until you find a name that works:
Thesaurus.com
This may take some time. You'd be surprised how many great & unique names are already taken. Don't get discouraged, you'll succeed eventually. You can register a trademark fairly inexpensively at:
LegalZoom
A caveat: I'm not sure how international law works in this regard. Sometimes you'll see businesses with the same name registered in different countries. I suspect that if you're doing business only within your own borders, no one will care - unless you decide to call yourself "McDonalds Hamburgers" and get on the company's radar screen. :-) Here's a site with a lot of info on trademark law in the USA and in other countries which I haven't had a chance to check out:
All About Trademarks
Vasily
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