Do I need a domain name to have a ZIP site?

No, but it's a smart idea. We can provide you a name like http://yourbusiness.bulaworks.com, and this would work without the need for you to own your own domain name. But why do that when we will provide a free domain registration with your ZIP site? We will help you locate a domain name and then we'll register it for you for the first year. Having your own domain name also makes it possible for us to offer you email service at that name.