Hi all again,
it appears I did something wrong during setup. I still don't know what it actually was, but setting up the address field in the realmlist database table for the realm to the external IP address (or the hostname rather) did work now. I can access the server from that hostname when I am outside of my LAN and I can also access the server using its local LAN's IP address from within that LAN properly.
I can confirm one entry in the realmlist db table is enough for that. The field "localAddress" is set to 127.0.0.1.
Sorry for the senseless post.
Hannibal