CLM should be able to handle FQDN in the complete eco system. The customer needs to have FQDNs because they have several customers configured on the same CLM instance. It should be possible to have same server names for different customers which means they are only unique using FQDN (as every customer has different domain).
Furthermore no DNS search suffix for each new customer domain is needed on the BSA server.
A possibility could be to use the custom hostname advisor. But currently both the VM Name and the Computer Name inside the VGJ are set to the same value (FQDN), which doesn't work as Computer Name needs to be the short name.
Some more thoughts in attached PDF.