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: YourName@YourName.com Simple, elegant, and much more effective than: firstname.lastname@example.org