I understood anonymous setting a little bit different.
Answers to the questionnaire are anonymous, not connected to any user.
However it would be fine for me to see non-respondents and be able to address them individually (not in punitive way of course , just to encourage them to fill the questionnaire).
Or other situation when new users are enrolled in the course, I would like to send them a message about questionnaire, not sending any repeating messages to users who already have received the message but not completed it.
I understand your point of view as well. You see anonymous as to hide who has not completed the questionnaire.
Does your plugin track, to whom the message has already be sent?
Then maybe there would be another option "Send message to new users" or something like that, to be completely anonymous.
What do you think about that?