The name that a business uses to identify itself is called a "trade name." This is the name the business uses on its invoices, letterhead, and signage. Technically, a trade name is not considered a trademark or entitled to protection under trademark laws unless it actually adorns a product or service.
If a business does use its name to identify a product or service produced by the business, the name will then be considered a trademark or service mark and be entitled to protection (if it is distinctive enough). For instance, Apple Computer Corporation uses the trade name Apple as a trademark on its line of computer products.
A trade name that is not used on a product or service may be given some protection under state and local laws (through corporate, LLC, or fictitious business name registration) or be protected against a confusing use by a competing business under federal and state unfair competition laws.
For information on choosing a name for your business rather than product or service names, see the area of Nolo's website on Your Business Name.