This isn't really the forum to be asking this question (ask over in TCP/IP or DNS forums).
But, to answer the question, you can have your own domain name on an intranet, as long as it isn't connected to the Internet. You wouldn't want to conflict with, say, scientology.org, or you'd risk getting sued.
It is possible for your intranet to be connected to the Internet, but you need to configure the DNS servers to not send any information with the outside world. You still want them to receive info, otherwise you couldn't surf.
You need to talk to an experienced network engineer (I am not one!) to get this set up correctly.
Chip H.