Computer with a domain name is called a

A domain refers to a group of computers that are part of a network and share network resources, like your home computers all linked together sharing a printer. The user logs in to the domain and gains access to the resources. Several systems may be involved. The computer itself is referred to as a server.

In general, a domain name represents an Internet Protocol (IP) resource, such as a personal computer used to access the Internet, a server computer hosting a web site, or the web site itself or any other service communicated via the Internet.