…because you are tweeting under your own name (or one easily attributed to you) and clients, bosses, customers, etc., are showing up on Twitter. I’ve had this discussion a few times and helped a few people make the change. This may sound odd that I’m discussing this since I’m still tweeting under my name (or at least it appears that @joeschmitt is Joe Schmitt), but I’ve helped my own boss and a few others with success.
If you change your user name, all your followers/following will stay. However, if people manually type in @oldusername it will not get delivered to you, and there’s probably some of that, though probably most click on the reply button. People on text or crappy phone apps are the ones you’ll lose.
Also @mrsjoeschmitt is already taken so you can’t change your user name to that.
So aside from telling everyone “this is @oldusername” when you change, also go register @oldusername again so you can check it once a day to see if you’re getting any tweets or DMs. Also check once a day at search.Twitter.com for @oldusername to see if people mention the old you.
I’ve parked @joe_schmitt and @joescmitt because people misspell it occasionally and I want them to find me. You don’t want to be found, so you’ll park it to watch for strays, not forward traffic. Don’t follow yourself because that’s a clue.
For your new user name you need to stop using your name in the name field too. [Your Real First Name Only] might be fine but why invite trouble? Also no pictures of you that are identifiable. But you probably figured all that out already. What you may not have considered is whether you should take the same precautions with your blog - point it to the new user name and take down any specifics from the about page and probably the photos. Take a cue from @mimismartypants whose real identity remains unknown even after her blog got published as a book.
Depending how deep you want to go, you could put a few innocuous tweets and your real picture on the dead end @oldusername page, so that someone looking for you on Twitter finds you and stops looking without realizing this is not the real account.
Finally, probably you should once a day for a few days remind people that this is you because not all will catch it the first time. Make sure to reregister for Favrd too, because otherwise I’ll miss all those stars you give me. And if you are on anyone’s Follow Friday list, then make sure you tell them personally so you don’t end up crossed out like @moelevin did.