Hi Christian,
Is the vRA 8? We ecnountered the same problem, and this is what I found. Note, I am new to vRA 8, so there may be better answers available.
Based on observation and reading, the domain name is viewed as a tenant. Therefore, an alias will not work because there is no tenant by that name.
Therefore, for our single dev instance, we have to use the host name. For production, we use a load balancer. In that case, we have a redirect that sends traffic from the alias to the actual tenant (domain) name. This works well for us. Also, be sure to include all Subject Alternative Names in your certificates.
Make sense? Hope that sheds some light on the issue.