Yes, California law, and the laws of many other states, already provide for that.
For example, in a California adoption, one of the consent papers you will be asked to sign at the time of the placement, asks you whether you authorize the State of California to provide the child with your name, last known address, and last known telephone number, should the child request that information upon attaining the age of majority.
Therefore, if you want your child to be able to find you in the future, the State will assist the child in finding you. If you do not want the child to be able to find you in the future, the State will not assist the child, and the State will respect your right to privacy. It is your choice.
Also, you can change your mind about that choice later, and you can write to the State Department of Social Services, specifying your wishes on this issue.