How Best to name my local domain?

Hello all... I have a domain, www.xyz.com, hosted on the internet. I have a server accesable as office.xyz.com. The server is the server for a whole office, and has 2 network cards. The external address coresponds to office.xyz.com. The internal is part of a 10.x.y.0/24 net... My provider at www.xyz.com hosts my email accoutns. (He provides virus scanning, and Spam controll) I also run a local email on office.xyz.com, since I don't want local email sent over the internet... Now to my question. What should the domain name of the office.xyz.com be? What should the doamin name of the machine in the office be? What is the "correct" way to set this up, (instead of the way I got it working now)? Jerry.