A stepparent adoption occurs when your spouse adopts your child. When this happens,
does the child's social security information get corrected to reflect the new legal father?
After a stepparent adoption is finalized in court, the child's birth certificate is usually amended to reflect the new legal parent's name. Once you receive the new birth certificate, you will need to take it, along with a certified copy of the Decree of Adoption, to the social security office.
When you arrive at the social security office, you will then ask them to change your child's social security information to reflect who the new legal parent is.
So that's the way that you change the social security for your child after the stepparent adoption is finalized!