The article's not very clear, though -- the implication to me seems to be that Facebook wants the information, but you're still free to use pseudonyms on the service itself to keep your name private.
Some Japanese people have major problems with revealing their name -- either part of it -- online, though. It's not something I've ever encountered in America outside of, say, 1998.
On the other hand, it might help to add some context that, before Facebook, there was Mixi, which requires you to have a working cell phone (with e-mail) for verification. Since you have to submit all of this data (and more) to get a cell phone in Japan, you're already pre-verified if you have one.
Not that there's anything wrong with that. Seriously, why is it so problematic if people use names they chose for themselves? There are even countries where it's a very bad idea to go online with your real name for fear of government persecution or other repercussions. Is Facebook going to enforce ID papers on, say, Egyptian dissidents as well? Sure they like to link all accounts with physical persons as intimately as possible, but it's not exactly in the best interest of their users.
