Ah, I see. Thanks for clarifying. Is it too much to ask to fix this so a public user's name too gets displayed in the notification?
I mean, there is an input that a public user is required to fill out when posting a question which would be only logical to use exactly for that:
<input type="text" name="jform[created_by_name]" id="jform_created_by_name" value="" class="inputbox required" size="20" required="required" aria-required="true">