Acomputer with a domain name is called what?

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.

so its called a server

It's called a server!
Hope this helps :)

Mouse and keyboard and software password data and the field codes

Wifi router/