I tend to agree with ModelWorks here. I feel that a lot of this is people over-reacting to a very basic part of all social interaction with other people - the knowledge of what your name is.
Almost no one is afraid to introduce themselves to another person, or be introduced by someone they know. The whole point of having a name is because of the need for it in social interactions. If you never talked to or interacted with other people, you'd have no need for one.
For better or worse, the internet has introduced people into a way to have real social interactions with others without the need to show who you are, generally resulting in people doing really mean and stupid things and then hiding behind their anonymity. The WoW forums, where virtually anyone who has been there knows is a cess-pool of attitudes, insults, and flaming, are trying to shake off that very problem by forcing people to fess up to their behaviors in a public manner, and as someone who has read and posted there - I'm all in favor of anything to clean it up.
Am I afraid of people knowing who I am? Nope. I surf WoW sites at work. My co-workers know I play, and many of them play too. I am not afraid to show people my name, even though it's fairly uncommon. I don't plan on being a jerk to people on the forums or in games, therefore not giving anyone a reason to WANT to try to find out who I really am.
I have been assaulted online previously. Someone has monitored my chats, emails, websites visited, and sent the results to others in an attempt to hurt me. And you know what? It wasn't an anonymous stranger online. It was my ex-girlfriend. I am still not sure how she got access to all of the stuff she did. But even so, I am not afraid of changes like this.
I don't believe it will result in some free-for-all of stealing identities, stalking, and harassment. I think people who claim it will are being a bit paranoid. It's your name. It's not your Social Security number, home address, phone number, and associated picture. Most people who read your post will not care who you really are. I could, very honestly, write a program that randomly assigns common first and last names together, and correctly guess the name of many people who play WoW. And I would know exactly as much as this RealID is going to tell people, except for the content of a post they might make.
If you don't want to show your name, that's fine. Don't post. You can still play the game. Just don't use the official Battle.net forums. Stick to fan sites and you'll still get everything you need, including support most of the time.