I am writing on behalf of a teenage girl who is about to give birth to a daughter. She is no longer in relationship with the baby's father and doesn't know whether to list him on the birth certificate. She is also considering moving back to Mexico (her country of origin). Someone told her that if she lists the baby's father and includes his last name in the child's name, she would have to get his permission to take the child out of the country. Is this true? What are the short and longterm ramifications of listing the father or not listing the father?

No that is not true, no matter if the father is listed or not, if the father goes to court and gets a custody order, he can ask the court to not allow her to move out of state. The Father can do this no matter if he is listed or not listed on the birth certificate.