https://www.computer.org/csdl/proceedings-article/hicss/2012/06149194/12OmNyKJiDq doesn't support my claim since on the aggregate level it's reduced and on individual level it remains the same. But to not be too biased (by my own claim), thought it was worthwhile to post it. They do say here that it only reduced malicious comments by 0.9% (so it didn't increase).Here it says it doesn't help. This article says discrimination increases, but I can't find the original source. They say real names are better then full anonimity, but worse then pseudonimity.

But searching for the right study, I can't seem to find it. Only news articles claiming it, but that's not much of a study. So maybe I shouldn't have said it increases, but it doesn't decrease (depending on which study and which aggregate level you look at). A lot of articles point at facebook where people need to use their real name but still post a lot of unfriendly stuff.