Like any trade name, logo, or brand name, your domain name represents a part of your business identity - something customers and business associates can recognize, remember, and positively associate with your services or products. Registering your domain name will at very least prevent someone else from using it. More important, however, is that with your own use on the Internet it becomes a constant positive reinforcement.
With your own domain name, access on the World Wide Web becomes a simple matter of entering Yourname.com. No one has to write it down, they remember it.
Similarly, every Email message affirms your name as your address becomes you@yourname.com. - simple, elegant, and much more effective than you@someunrelatedprovider.com.
Also, by doing business under your own domain name, a good service provider can offer you multiple Email "aliases," all going to a single or multiple parties. They can even be forwarded to people outside your physical location.
Finally....ITS PORTABLE! If you've ever had to change your service provider, or even move your physical business address, you know what an incredible hassle it is to notify everyone. Remember, that without your own domain name, your Internet address is tied to that of your service provider. Thus, if you want to change providers you also change your Web address and probably Email address as well. Consider for a moment: Are your ready to print new cards, brochures, etc., or contact all your clients, suppliers, business associates, etc. of your new address? Can you even remember them or reach them if you want to? And, every day you're in business the list gets longer. Your own domain name lets you avoid all that, giving you a permanent Internet address. You can change your service providers every month if you want, and your address will always remain yourname.com.