You are thinking it would affect much more than it actually would.
If there was a valid and real birth certificate registered with the state of birth, then that is still valid.
for all intents and purposes she has lived under an assumed name that doesn’t match her actual birth certificate. It really won’t change much. In many states a person can assume any name they wish whenever they wish. This isn’t much different.
But she has the benefit of everything in her life being under her assume name. A few corrections of vital statistics and away she goes.
If the legal parents didn’t obtain a SS number, then there is even less mess. Her current SS # would still be valid and the fact her entire life was lived using that number, all of her earnings would be properly credited to her a Account although under the assumed name. That can be fixed. If they did obtain a number and the kidnapper also did then the SSA can deal with that as well. There are actually some people that are issued a new SS # for various reasons. The SSA overcomes the issues involved.

