"Legally," within the US jurisdiction, the thing that is forcing you to keep "your" first and last name is the fact that you keep using those as "your" name. It all started when you received you birth certificate, then your driver's license, your bank account, etc. You are using an identity of "theirs" for "benefits" (licenses, permits, accounts, etc) that ultimately they control. The more benefits you use, the more easily you prove "your" identity. Typically, stolen identity cases are not always easy to prosecute.

The same thing could be done with different identifying documents. If you found a birth certificate that was nearly the same age as you are (or, as you think you are since you are not aware of the actual date of your own birth due to lack of mental capacity) and did not already have someone using it, you could start over again with that identity.

As I said in my other comment, I recommend people read The Paper Trip Series. They can be bought all at once or one at a time.