Transparency is desirable, but as any woman can tell you, you certainly have to protect yourself.
Des Walsh writes discusses anonymity from a practical sense, but so does Jennifer Woodard Maderazo at PBS.
The dilemma is between being known and credible, and being 'found' and frightened.
Obviously I'm a huge advocate of pen names. I have a history which makes them second nature and deal in a subject matter which makes one mandatory. So I began my life here on the Internet with a working name ~ a professional name I work under. (Gracie Passette, not just The Whore; I find the latter fun.) And I advocate pen names for anyone, in any profession. I don't believe that pen names make you less credible.
(I often think it would be great if you could literally make a name for yourself in your 9-5 cubicle, and say work as "John Peterson" rather than use your birth name. It makes it so easy to un-plug at the end of your work day when you stop being "John" and start being David aka The Real You.)
But if this doesn't sit right with you, or if you've already begun your career with your real name, for heaven's sake be careful about it. Consider what you share, how you share it, and with whom you share it. Tell the truth, but cloak what you can.
It's like dressing to tease, but still allowing for some modesty.
(In truth, many bloggers etc. use their real names not for their current level of credibility, but for the vanity of it).
You aren't faking anything, just being discrete for safety reasons. And anyone who thinks you have something to hide, some hideous skeleton in your closet or facet of your life you are trying to hide, is well... Partly right. Maybe not about the skeleton. But you are trying to hide some part of yourself so that you can be safe and live your life. (As can your family and friends.)
Not using your real or birth name isn't any different than electing not to put up photos of yourself. But then again by the same token, don't use a name which belongs to someone else or describe yourself (character, integrity, knowledge etc.) other than what you are. That's like using a photo of a model; that's misrepresentation, lying.
Sure, when you become famous you won't be easily getting that table at (insert whatever hot spot for dining you'd like), but then you won't have someone following you to your home either. Or at least you've made it more difficult for them to do so.
Being accessible is a huge part of credibility; but that doesn't mean you must allow anyone, everyone, into your home.
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