You should file a paternity lawsuit to establish yourself as the father. On the issue of rights as the father, paternity testing can be compelled by the court if mom or you request it. You may also ask to have your surname on the child, and that request will most likely be granted by the court. This is an old Texas common law rule that the father has a protectable interest in the child bearing his surname. In re Baird, 610 S.W.2d 252 (Tex. Civ. App. — Fort Worth 1980, no writ). Mom could ask that the child’s name be hyphenated with yours, or request that the father’s name be a middle name, but these requests would be at the judge’s discretion. You may request to have access to the child and a regular visitation schedule. You would have access to medical and educational records of the child. You would have the right to direct the moral and religious training of the child while in your possession. These are a few of the rights a biological father may be awarded.