Found a solution.
Inside a CentOS 8 container you find in
/etc/sysconfig/network-scripts/ifcfg-eth0
the term
DHCP_HOSTNAME=`cat /proc/sys/kernel/hostname`
If you replace it statically with your hostname like
DHCP_HOSTNAME=“test02”
everything works fine.
@stgraber could you tell me what to modify in my installation to create the DHCP_HOSTNAME the same way as HOSTNAME or might it be advantageous to modify the CentOS 8 container in general?
NBB: In CentOS7 the substitution worked fine. So it might be specific for version 8.
On the command line a cat /proc/... works fine, but not inside ifcfg_eth0