In order to do what you are asking, there first needs to exist an anonymous user.
Assuming this user exists, there are just a few steps:
1) modify the comment form to include the anonymous check box.
2) detect whether the box is checked.
3) if the box is checked, use the comment_save_pre filter to change the user’s info to that of the anonymous user.
Hope that points you in the right direction!
EDIT: Be sure that you have the comments settings in your dashboard only allowing loggedin users to comment.