I have computer with a host of DumbServer. When I try to connect to http://DumbServer or use DumbServer in Putty, it doesn't work. If I use the IP address, everything is fine. How do I set it up so that DumbServer works without having to add the entry into the hosts file for every computer?
Add a record to your local DNS server.
Do you have an internal DNS server? If so, you'll need to add 'DumbServer' as an A record in one of your DNS zones, pointing the IP address to the IP of that server.
If you add the record to a DNS zone which matches a DNS suffix configured on your computers, you will be able to address the computer using simply http://DumbServer (rather than http://DumbServer.domain.tld)
If you don't, I do believe that with an OpenDNS account, you can configure an alias for 'DumbComputer', which would be resolved (by OpenDNS) to its internal IP. This would, however, require you to point all your computers to the OpenDNS servers.
You can use DNSMasq, e.g.: http://www.dd-wrt.com/wiki/index.php/DNSMasq_as_DHCP_server
Cheers
Easy answer, just add an entry to your C:\Windows\System32\drivers\etc\hosts file. This will allow applications on your workstation (and only your workstation) to use the server's name instead of it's IP address.
Less easy answer, add an entry to your DNS. Others have already posted answers on how to go about that.