David,
It sounds like there is an issue in your DNS configuration. ThinPro can see the Domain Controller and knows what it is (hence the population of the IP address in the domain field) but DNS doesn't appear to be converting that IP address into a Hostname. Since it only appears to do that in the password change dialog, I'm thinking it's one of those slap your own forehead configuration issues. Something appears to be preventing the DNS from assigning a hostname before the user is fully logged into the Thin Client.
My advice would be to double check your configuration in the following places on the T5565 (you need to be in Administrative Mode to do these):
Control Panel -> Network -> Security Settings -> Authentication
Control Panel -> Network -> DNS
Control Panel -> Management -> AD/DNS Manager
In the AD/DNS Manager look for Update...
