Comment Because you need your real name for some things (Score 2) 602
The difference is you can choose to not mention your username in, say, a job application, and there is no way to link your real name to your activity online (assuming you haven't done anything stupid that links the two). You are also under no obligation to provide your username on your drivers license, legal documents, or when checking into a hotel.
Setting up a new username and account with no connection to your previous online presence is also much more simple and effective than trying to set up a new and unlinked real-world identity.