To change Confixx's hostname (i.e. reaching the login under a different / new domain) is quite complicated. 

Proceed as follows:

1. Log in to Confixx as administrator
2. In the left menu click on "Einstellungen" -> "Standard-Domain"
3. Enter the new domain here and confirm your input

4. Conduct the Confixx update script.

Confixx should then accept the new domain as standard domain.

WARNING:

Versions 3.1 and above do save and display the new standard domain in the database but it doesn't work.

Reason: It's not entered as ServerAlias in the confixx_mhost.conf file.
Corrective: Edit the file /etc/apache2/confixx_mhost.conf and paste the following line under the "ServerName" line in the <VirtualHost xxx.xxx.xxx.xxx:443> area: ServerAlias the_standard_domain.tld, where standard_domain.tld has to be replaced with your domain.

This solution may not be very smart since the mhost file could be probably overwritten by Confixx anytime, but it provides a remedy until the error is fixed.