I was reading a book "Leveraging the Impact of 360 degree feedback" and was interested in the author's focus on anonymity. For them 360 degree feedback required anonymity even to the extent that they saw a downside of narrative feedback being the potential for identifying raters.
One of our largest clients has just run 360 feedback where the raters were named. I have not heard of any issues at all nor is it obvious that the ratings were effected by the lack of anonymity.
Our experience is that anonymity is more worried about than it is an issue in reality. But confidentiality is crucial. My report is confidential to me - how I rated someone else is something I'm usually more than happy to be exposed.
I believe this distinction is important. If a rater needs to hide behind anonymity it implies they would be uncomfortable giving this feedback to the person directly. We see 360 feedback's potential in its ability to give rounded feedback in a straight-forward manner - we don't see it as a route for people to say things they wouldn't otherwise say. We know that this happens and sometimes it is a good thing but generally anonymity is overplayed.
Keeping data and reports confidential is another story and crucial to the success of the process.