Yes, this is a extremely common practice it is called a Shared Web Hosting
In name-based virtual hosting, also called shared IP hosting, the virtual hosts serve multiple hostnames on a single machine with a single IP address. This is possible because when a web browser requests a resource from a web server using HTTP/1.1 it includes the requested hostname as part of the request. The server uses this information to determine which web site to show the user. When you register/purchase your domain name on a particular "registrars name server", your DNS settings are kept on their server, and in most cases point your domain to the Name Server of your hosting provider. This Name Server is where the IP number (currently associated with your domain name) resides.