Whether you are biologically tied to the donor egg or not, your name is placed on the birth certificate. Both Intended Parents are placed on the birth certificate and there is a form filled out after the birth of the child. Your Indian lawyer or clinic rep will give you this form and then it is sent to the municipal authority and you will get the official birth certificate within 3-5 days. It's pretty easy, so long as your husband is a U.S. citizen, as at least one biological parent has to be a U.S. citizen to give the baby U.S. citizenship. Otherwise, you better hope that the embassy isn't requiring a DNA test, which they do in some cases (especially if the couple has different citizenships). Hope this helps.