The name of your business serves various crucially important purposes, not only for top-of-mind awareness, but there are also SEO and web optimization benefits to consider when coming up with your ideal business moniker.
People have goldfish minds on the internet. Give your business a long, multi-syllabled name and those who come across it may not even read it to the end - let alone type out your twenty-character domain name to reach your website. Keep it short and memorable, and think about something visual that people will remember and which can inspire a striking logo.
Don't forget, though, that you're going to need to use your name offline, too - in fact, you're going to be saying that word or phrase every day of your life for as long as your business flourishes. Pick something that's pleasant to say, for which the pronunciation is clear - and which isn't easily mistaken for something else. Amazon, for example, used to be called Cadabra; the change was made after they realized people were hearing it as 'cadaver'.
On a technical note, you need to make sure that your business name is not already in use, and that decent URLs and social media handles are available for it. You don't want customers to be accidentally dialing up a rival company or some random civilian who happened to choose your business name as their Twitter handle. Hopefully, if you pick something special and unique, this won't be the case - but you can find out on namechk.com before you make a final decision.
The wise folks at the Business Backer have put together a new infographic to give you full guidance through the process of choosing your new business name. Pay close attention, and you should be able to come up with a marketing winner that will sell itself.