I have two computers, Windows XP and a newly installed Slackware machine which I already like much better.

Both machines can ping each other with IP address
Only the XP can ping the Slackware machine using the hostname

Pinging from Linux to XP results in a message about unresolved hostname and IP Address

From what I have read, I need to set the hostname to point to the IP address in the /etc/hosts file??? I don't see how I can do this if the dchp is allocating addresses dynamically?

The machines are connected via a linksys ethernet 10/100 hub and internet access does not (will not) exist.

Also, I setup samba and can view the files on the Slackware machine from XP, so I know I am close to getting this to work.

Thanks in advance for any help.

If you've only got a few systems, using static IP/Name combos is perfectly reasonable.
You can either

1. disable dhcp entirely and use static entries in /etc/hosts (or equiv on XP)
2. have a dhcp server, but use the option to set static ips according to MAC addresses