I recommend going with your name for Twitter (wish I had but didn't as a newbie). Use your real name for a personal profile on Facebook and use your business name for your Facebook Fan Page and be sure to include some keywords in the title of your fan page (again, I didn't do this at the time b/c I didn't know about it...now I make sure to do it for all my client's fan pages.)
I have a myspace with my business name....but NEVER use it...don't even have any "friends" on it
LinkedIn should always be your real name with your business name listed as where you currently work.
Try and brand your IDs for different social networks to be the same as closely as you can...for example, almost all of my social network accounts are jkvirtualoffice- this includes Stumbleupon, YouTube, Delicious, this forum and others.