When you go to court to change your name, petition the court to seal the record. Talk to a lawyer in your jurisdiction about how to do that.
Aside from that,
1. Move to somewhere where no one knows you.
2. Make absolutely sure there is no connection whatsoever between your internet presence under your old name, and your new name.
3. If someone wants to find you badly enough, they will find you. You cannot change your social security number unless you are a documented victim of identity theft.
4. If you have existing credit or bank accounts under your old name, pay them off and close them. Then set up new accounts under your new name.
5. Job history/resume is the big problem. If you have a long gap in your resume, or your job history starts when you assumed your new identity, a lot of employers are going to start wondering if you just finished serving a long prison sentence.