This is the most confusing registration process I've ever gone through. What's the difference between my username and my display name? Why does my username need to be a permutation of my real name? I'm not going to remember that! The first time I registered, it told me I already had an account on these forums and asked me to log into that, but I don't know what credentials I used.

Not sure i understand. Is that a complaint or a question? Because obviously you now have an account that seems to work.

As for the obvious questions, the difference between a username and a display name is - like you already noticed - that the policy says a username should be build upon your real name. This has historical reasons, as identity.kde.org (our central login system) was initially done for KDE developers, which need to be identified by a real name.
Obviously this isn't enough, so when several of our platforms moved to the central login system we offered the choice to additionally choose a display name. Not everybody wants to have the real name visible, which is fine. Still, the first policy applies for maintenance reasons.
Now you might wonder why so complicated. The central login enables more than just a forum login. It holds access control lists for the developers, logins for the forum, the wikis and several other places. Other platforms following.

Hope that helps.