Certificate doesn't verify

[Paul Douglas Franklin]

I have a user who connects from on or off site using Outlook 2003.  He 
keeps getting the following message:
"The server you are connected to is using a security certificate that 
could not be verified.  The certificate chain processed but terminated 
in a root certificate which is not trusted by the trust provider.  Do 
you want to continue using this server?"
When my Thunderbird complained, I simply told it to accept the 
certificate, and it did so.  But Outlook doesn't seem to want to 
remember that.
I believe that it has to do with the name of the server vs the name on 
the certificate.  Would this be a likely cause? 
If so, it's my error:  I was deciding between two different names and 
just didn't enter the correct one when I created the certificate.  How 
do I ascertain the name on the certificate?  And can I create a new 
certificate, or do I need to change the name of my server?  I can think 
of three places where I figure the name should match:  DNS, host name, 
and certificate.  Is this correct?
If the non-matching names are not the problem, what would it be?
--Paul

-- 
Paul Douglas Franklin
Computer Manager, Union Gospel Mission of Yakima, Washington
Husband of Danette
Father of Laurene, Miriam, Tycko, Timothy, Sarabeth, Marie, Dawnita, Anna Leah, Alexander, and Caleb