I know that a couple of questions regarding anonymous posts have been discussed recently, but they've been in the spirit of encouraging impartiality when voting.
However, sometimes we just have a burning question about something we might think is embarassingly simple or easy. We might have given our SO username to prospective employers, or generally don't want to lose our street cred with the community. However, these could be questions that add real value to the site... through search and such.
There could be a "anonymous" questions section of the profile that simply gave the number of questions and Rep earned, without naming and linking to the questions.