It's a good thing to be able to identify people commenting on your blog. As the owner of the blog, you are responsible for policing it's content. Now that you have chosen to include names of posters, I think you now must hold yourself to a higher standard of moderation and yes, that means censorship.
I do think that you'll find fewer people posting and fewer people reading over the next few months, but nothing ever stays the same.
Say Hi to Erin and the munchkin.
Does anyone else get a creepy feeling when someone who won't reveal his name presumes to comment on personal details of my family? And creepiness aside, what good is a "Hi" if we don't know from whom it comes?
Me: "Someone says hi!"
My love: "Who?"
Me: "I don't know. Just someone."
My love: "?!?"
As for the actual content, I fail to see why Anonymous would feel the need not to attach her/his/its name to the comment. Other than being afraid of publiclty demonstrating her/his/its failure to grasp the nature of online media (no, I'm not responsible for commenters' statements; no, banning anonymi is not censorship; and no, my standards are fine right where I put them, not where you wish to impose them), what is Anon so afraid of? Retribution? Since when did I become one of Madison's country club Illuminati?
For what it's worth, it's far too early to determine the effect of the new comment-nymity policy on readership (though the poll is running strongly against it—cast your vote!). But Anon fails to understand that the point is not raw numbers. Suppose banning anonymous comments drops comment volume and daily hits by half. Do I really lose that much if all those folks were coming here just to read and post disembodied snarkiness in the comment section?
Compare it to a party: would you rather throw a big beer bash for a hundred people, a bunch of whom you don't know, some of whom break your dishes and behave in other unneighborly ways? Or would you prefer a smaller gathering of friends and neighbors, all of whom get to know each other on a first-name basis and have respectful, enlightening conversation?
Or more simply, what do you prefer, quantity or quality?
By the way, just yesterday, I found my conversations here with Stan, Tony, John, and even Tim, with whom I strongly disagree (they are cool pictures), to be much more enjoyable and neighborly than some past mudslinging. Keep those cards and letters coming... but understand that I can't truly respect your words if they don't come with your name.
Update 2009.05.08: See also this commentary on anonymity, civil discourse, and the First Amendment by David Newquist of Northern Valley Beacon. An interesting quote from Dr. Newquist: "[T]he journalistic basis for attribution is that quotations are not actual unless their author is identified." Wouldn't you rather be actual?