Something doesn't sound right.
The common name on the certificate, '<CERTIFICATE HOSTNAME>' is invalid or does not match the server name, '<USER ENTERED SERVER HOSTNAME>'.
So the second host name in the warning message should be 'clientname.example.com' if that is the Host you've set in the Site Manager.
This should not happen, FlashFXP should verify that the hostname I entered in the profile matches the Common Name or Subject Alternative Names of the certificate. It does not matter that the hostname has a CNAME record in the DNS.
It shouldn't, since we compare the host name entered by the user and not the name or alias returned by the DNS server.
Can you send me a private message with the host name so that I can perform a connection test to fully diagnose the situation.