Hi - my name is XXXXX XXXXX I'm a Family Law
litigation attorney. Thanks for your question.
Your husband giving up his parental rights
BEFORE the child's birth is not legally effective. He could not give up his rights legally until the child was born. Thus, your husband should still have legal rights.
As for changing his name, if the child and his mother and father (if there is a father named on the birth certificate) are agreeable to changing the child's name to your husband's last name, then it is a fairly simple process and just takes a petition for name change
. Here's a link with a sample petition: http://www.texasbar.com/Content/NavigationMenu/ForThePublic/FreeLegalInformation/OurLegalSystem/NameChangesInTxpdf.pdf
However, doing this will not make your husband legally considered as the father of the child, and would not create any legal relationship.
If your husband wants to be the legally recognized father of the child, he would have to file a petition for paternity
to be established by a DNA test. If the DNA test results prove that your husband is the father, then he would be considered the biological parent
of the child, a new birth certificate can be filed, etc.
Also, it is POSSIBLE that if your husband is determined to be the father that the mother can seek back child support from his birth up to the present. The mother would have to seek to do this before the child is 18. Thus, there is a possibility for this to happen.
If you were to wait until the child turns 18, he can file a petition to change his name without his parents and you should also not have any threat of child support being sought.