Rather than just having the options for how you can post as:
Logged in User
how about adding:
name: _______ email addr: __________
They will get a message after their post, saying:
An e-mail has been sent to your account. Please reply to the e-mail and hit send to verify your e-mail address. Your post will be added once your e-mail address is verified.
These posts would show up as :
Although replies to their post would be sent to them in e-mail, standard users would have no way of determining their actual e-mail addresses. Administrators would be able to look up which e-mail address such posts came from, however.
I would also add a field under anonymous, allowing anon people to post with a name. These would be shown in posts as: