For starters, no matter who you are, you will more than likely be working without an original birth certificate, unless the adoptee is born in one of the states that are providing copies of the original birth certificate. If you were not born in one of these states it is highly unlikely you will get one. In a majority of the states the records are closed to adoptees wanting their original birth certificates, but it never hurts to try
Natural parents cannot find out their "child's" name after adoption either from the birth certificate as they are not entitled to one, having given up rights to the child. The adoptee gets an amended birth certificate listing only the adoptive parents, and uses his or her adopted name. Natural parents will get nothing if they request the birth certificate post-adoption because, having relinquished parental rights they are advised they have no further interest in the birth. Depending on the natural mother or anyone who may have influenced the process, the natural father's name may or may not be present on the original birth certificate. Sometimes for financial aid or to avoid a paternity dispute, it was deemed best to not name the natural father.
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If you are an adoptee, ask for your birth certificate anyhow. Get whatever info you can from elsewhere and you may be able to make some assumptions, you might get lucky when you get non-id with some critical tidbit, you might get someone who blurts something that will help you build a foundation for your search. The tips in the following blogs should help you do this.
During your search it is also important to educate your self on adoption issues and speak to other triad members who are searching and have searched and are in reunion. This is your time to prepare yourself for whatever could happen.