Read, read, read There are many books about searching and reunions. You will learn about other people's searches. Keep your mind, heart, eyes and ears open to the message of each. Begin at your local library. If you are an adoptee, ask your adoptive parents.
Most adoptive parents expect their children to ask for information.
Some offer it but most must be gently confronted. The best outcome should be that your parents share all the information they have, which sometimes includes the name and more. If not, they can direct you to the agency or intermediary who helped make the placement. Be very circumspect and thoughtful about why you are searching. Medical information to survive is probably the most compelling reason to search.