Exactly. Some states even reissue for "transgender" to reflect the "new" sex and name.
In my view, a BC is a historical document of fact. They should be immutable but amendable like our federal constitution so the original records of fact are preserved. Anything less is just rewriting history.
When a child is adopted, the child’s birth certificate will be changed to reflect that information. The nature of the changes and how they are made may depend on the state in which the child and adoptive parents reside. In many cases, the original birth certificate may be kept and sealed after an adoption and a new birth certificate may be created.
How is a birth certificate changed after an adoption?
After a child is adopted, most states will perform a similar procedure as follows:
If the child is from a foreign country, the parents will file the adoption papers from that country in their local jurisdiction when they arrive home. The papers will be handled by the district court to complete a certificate of adoption.
The same will be true of a child adopted within the US. The adoption certificate will be created by the parents’ district court based on those papers, regardless of their point of origin.
After the adoption is finalized and the certificate of adoption is completed by the district court, it will be mailed by the court to the local State Department of Health to be processed by the Registrar.
The adoption certificate will be used by the Registrar to create a new birth record. This will list the new adopted information, i.e. the names and information of the adoptive parent(s) as the legal parents of the child. The child’s birth date and other details may or may not remain as listed, depending on the circumstances of the birth. Information about the biological parents will be removed from the official record, and the new information regarding the adoptive parents will officially replace the original birth records, if any. The original records will be sealed and filed in confidentiality, only to be released under specific court orders in rare situations.
To ensure that all steps are completed smoothly, an adoption lawyer should be consulted during the process.