|So the simple answer is, use the IP. Personally, I never use hostnames for the very reason you're having a problem with it. Resolution problems never arise if you're using the IP.|
Having said that....
Is this an Active Directory domain, or is it a workgroup. If it's a workgroup, try making an entry for the problem computer in the hosts file on the computer you're trying to connect from and that should fix the problem.
If it's a domain then check the DNS settings on the computer you're trying to connect from and if they reflect the correct DNS server address, check your name resolution on the DNS server.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.