Why not just run it like this one? That's what people did back when the majority of boards didn't support user registration or admin functions beyond deleting posts. I ran a lot of them that way and you'd be surprised how seldom user name conflicts came up, even though you could post with any name you liked. As admin you will see the ip addresses of posters, if you need to sort out who is who, and still leave registration as an option for those who want a unique, permanent, user name. If anonymity is your goal, leave the registration in place and provide users with a list of disposable email sites like Guerrilla Mail.

To set it up the way you want could be done, you would have to hack the code a bit, but it's possible. You will have a real admin nightmare when you are done. The end result would be a honey pot for spammers if it's on a public system. Good user names will get snatched up quickly, you won't be verifying email addresses so password resets won't be an option in many cases, meaning there will be more user names taken out of the equation as users forget passwords for accounts they create on the fly.

Knowing what your reasoning is for doing this would go a long way in helping you come up with workable solutions