How did the Germans find out the names of the Danish Jews?

The soldiers confiscated the list of names from the synagogue.

He turned to her and stroked her hair with his gentle hand. "This morning, at the synagogue, the rabbi told his congregation that the morning, at the synagogue, the rabbi told his congregation that the Nazis have taken the synagogue lists of all the Jews. Where they live, what their names are. Of course the Rosens were on that list, along with many others."