Hilda Bastian has published "Weighing Up Anonymity and Openness in Publication Peer Review" in Absolutely Maybe.
Here's an excerpt:
There are some consequences that flow inevitably from the choice of anonymity or naming, like workload for journals, or the ability for peer reviewer conflicts of interests unknown to editors to be revealed. I'll come back to that later. But first, what evidence do we have that masking the identities of authors and peer reviewers achieves what it is meant to? . . .
So I've taken a deep dive into this literature. I found 17 relevant comparative studies, 12 of which are controlled trials. The quality of these studies varies greatly, especially the ability to control for variables. Some are in hypothetical situations. But there are some very good, decent-sized trials.