After the Image-Creation my Master-Machine comes up with the same Machine-Name it has prior to creating the Image. This is, according to your post, normal behaviour, right? The custom Workgroup-Name is also the same after Image-Creation and also it is still DHCP. Is this normal behaviour too?
Yes this is normal behavior.
And what about the (different) Machine I deploy this Image to? I see even the same there, same Name, same custom Workgroup and DHPC. I also see no OOBE-Screens after first boot.
This is not normal behavior, you should see an oobe screen (depending on the answer file you are using) after you deploy the image to a machine. The name, dhcp config and workgroup are all changed with the GSS configuration task (if you so choose). Sysprep creates a generalized image that removes the SID and assigns a volume license to the image for deployment.
I would check the panther folder on your client machine "C:\Windows\Panther" for log files that may indicate why sysprep is not running properly. Should see a file called "Setuperr.log"
You can also run sysprep manually from the location "C:\Windows\System32\Sysprep\sysprep.exe" and see if sysprep will run properly manually.