name/env variable for networked computers

I have a couple of computers running on a local network, connected via a Technicolor 105+ TC8305C (xfinity router) most are wired, but 2-3 are wireless. My ISP is comcast. I think we use cable. Everyone uses Norton 360 Premier Edition.
My IPCONFIG -all - Pastebin.com

^That was because of this

My problem is that I want to reference another computer, PERSON-PC, to use the msg command, and some other thing I forgot. I have remote desktop and security setup, preferably I want to setup some environment variables.

Your DNS Servers are pointing to external servers.

This will make internal DNS queries - I.E. PERSON-PC get resolved on an external server.

Your DNS Server needs to be changed to your local router.

As you are getting DHCP from 10.0.0.1, I wuold suggest changing the LAN DHCP Settings to give out the router as the DNS Server. OR Setup static IP Addresses.