I did everything and ran the script.
Then I checked for the result with PHP MY ADMIN.
OK, the names got put into the Anon-Field. And in those cases the Reg. field was "n".
But opening a thread in Threads (flat mode) shows the Poster-Entry in the summary-table in such a case empty. Ok, I open on of those posts and see that on the left side there is "non registered" written but nothing else: The Anon Name seems not to be displayed. So there is still a problem somewhere?
I have set: "unregistered username allowed and displayed": YES