Thanks for the answer. I can read German BTW (and speak it), its just I do not want to write it, I would make too many spelling mistakes.
The value you refer to is the external host name fritz uses for getting an external IP address. I meant the implicit internal hostname for the local DNS lookup, and more importantly, the local suffix it assigns to all other local clients.
I guess if I would use Freetz, and replace the DNS with DNSMASQ, I could change it there, but I was hoping to be able to change it on an as clean as possible Fritz.
Edit: Thanks sf3978
(I started typing the answer before noon, and only submitted after, so I did not see your reply yet)
Makes sense, just use the hostname command. Thanks.