This is very field-dependent. In mine (political science) it's routine to blind the reviews in both directions. In others, papers are reviewed with the author's

This is very field-dependent. In mine (political science) it's routine to blind the reviews in both directions. In others, papers are reviewed with the author's name and affiliation on the top. There is a further issue that if you're in a small-enough (sub-)field you probably know what other people are working on and can effectively unblind the authors anyway.