Step 11: Associating a domain to your witness node (optional)
Some people keep their nodes private and some people are happy to associate a domain to their node and make it public. For people who would like to associate a domain with their nodes, the below article will provide the details.

NO!!!! Not with your witness node. Another node that you keep lying around with the same specs with your node, sure. But not your witness node. You don't want to expose that to the public and cause any unnecessary issues.