This is ironically, one of the most difficult yet important decisions a business owner will ever have to make, especially if you are planning to use your company name as the brand for all of your products or services. As with any creative process, start with brainstorming as many names as you can manage. Try to make the names interesting, but not obscure so that people cannot relate. There are some exceptions to this rule (Google, or Yahoo come to mind), but unless you are planning to change the world, choose something that makes sense.
The next step is to check if these names have already been taken. Do a google search. Cross out ones that have already been taken. Then take your shortlist and do a domain name search to see if any of these domains are available. You may end up with very few or no available names at the end of this process. The best thing to do at this stage is “rinse and repeat” until you find something that fits and is available.
Company names that are one to two words at the most (are easier to work with on letterhead and logos). For instance, Canadian pizza franchise Pizza Pizza, grocery store Coppas (easy to remember), or connection names such as No Frills or Dollarama (associates “low cost” without saying it).
Finally look at registering your company. Look for existing trademarks or company names (NUANS search and reports). Create your business logo and website, and you are now officially in business!