No, you can not block anonymous users after you have already posted your question. However, if that user is behaving inappropriately and breaking the rules of the site, then you can report their comments and the admins will look into it. Otherwise, if they're just being annoying but not breaking any rules, you'll just have to ignore them.
After the question is posted, there's no way to go back and change the anonymous/no anonymous preference. You cannot block someone without knowing their username. Please report (click the flag) all posts that violate our guidelines and we'll take care of it.