Creating a live website only requires a web server. Though a website without a domain connected to it, will be much harder to access. As the website will only be accessible through its IP address. Although technically possible, you should almost always register a domain, when creating a new website.
Without domain names, it will not be possible for people to find your website and without web hosting you cannot build a website. This is why many top domain name registrars also offer web hosting services.