I don't really care so much. In the past, it was a bigger deal because people revealing their real names was less common. Now, because of the advent of Facebook and other such places forcing you to use your real name, it isn't really something to be concerned about.
All of the people/organizations who want to find out about me already can anyway. (Like Google, they have information on almost everyone that is spooky.) And most people on the internet are generally like most people in real life - generally sane individuals who keep to themselves and don't want to murder you with an axe or be a rapist or whatever.
I am more cautious about my last name though. I don't like to reveal that in public, but am fine with saying it in instant messaging after I've spoken to someone a few times. It's just a bit of that remnant of paranoia from the past staying with me.
What is my real name? Well, at the moment, it is Angela. But please, do NOT call me that. I am going to be changing it in about a year or so because I just hate hearing that name in reference to myself. Don't hate the name itself. I just dislike the person it makes me think of when it is said to me. It's a name I have grown to associate with a weak, shy version of myself who could do nothing in real life, and I would like to shed it.
I'll probably be changing it to Adele, so refer to me as that if you want to do real names.
Funnily enough, people have thought that Arylett is my real name. Which is entirely intentional. I wanted to create an internet name that didn't sound like your stereotypical internet name. Something that sounded like it could actually be someone's name. And because of the way the name is, I have learned to identify more with that name than Angela. So calling me Arylett is a great compliment, as you are addressing who I feel I actually am. I've probably been called Arylett more so than my actual name, because since the age of 14 when I first started using that name, I have socialized far more on the internet. Adele is something recent, but I'm also starting to get attached to it in the same way.
Yes, I am weird about names. But I find them to be very important. In meaning, in how they are spelled, and how they sound. To me, they should reflect a person accurately.