If your Athlon box has a private RFC 1928 address like 192.168.x.x or 10.x.x.x.x then you can configure a private domain/zone for it. But you don't have to.
You also can edit
/etc/myname and
/etc/hosts to change to a not so confusing names.
If your box has a public IP then you should use the official name that goes with that IP address.
See
http://en.wikipedia.org/wiki/Hostnam...lid_host_names for the character set restrictions for host names.