I found out that you can hide the names of the users that participated in the settings dialog.
I tried this and it's working pretty nice. In the answers an *** gets displayed instead of the name of the user.
When I reactivate the setting option the name is again displayed. So its just hidden and not removed.
Is there an way that the user name is not stored at all while participating the survey? It's required to meet our privacy standard on this survey due to the answers should be anonymous and not even admins should be able to see who provided the specific answer.