Finally I got it.
Our Hosting Provider (Host Europe) has an option in the Controlpanel for each server (virtual root server). On the page "Hostname / RDNS" there is an input field "Hostname:". I changed it to the correct value and now it works as expected.
Because this seems to be vendor specific feel free to delete my question.
I just leave it here in the hope that it helps somebody else ...
hellcode
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