Sadly, EULAs and the like tell them they can do this. Courts have upheld it. Which means taking them at their word is pretty much useless.
What? If the user who wants to participate in online discussions on a private company's web site agrees to a EULA that states that the owner of the web site reserves the right to change the conditions of using the site, then that's exactly what you signed up for. The only "sadly" involved is users sadly not reading what they agree to. Most people in the gimme-dat-free-stuff mindset don't think things through anyway.
Real names policies exist because companies say "what value can I get from selling the fact that SuitWrinkler53 commented on the website?" and deciding that they can't sell that information.
Or, if you're a publisher, those policies exist in order to spare the publishers huge ongoing legal expenses in dealing with inquiries and even subpoenas related to digging out real names or other information about trolling, libelous, or otherwise criminal users.
And then you realize they don't know much about the underlying technology, and are probably using something like WordPress.
No, then we realize that you're talking out of your ass and haven't bothered to so much as view the source on one of their pages in order to see that you're wrong. And that the paper - like so many who can't afford to go about it in any other way - are using a third party SaaS solution. Which means a single code base for many clients, which means no, customizing it for one customer isn't always desirable or even do-able.
They just have to remind you it's technically private property, and that the license says they can change the terms if they wish.
Oh, so you DO get it. What are you bitching about, then?