In Oklahoma, the mother of a child born out of wedlock has custody of the child until determined otherwise by a court. There is an exception for men who sign an acknowledgment of paternity and are listed as the father on a child's birth certificate. They have all the rights and obligations of fatherhood. You say the father "removed his name." I don't know what that means. It brings up other questions about acknowledgment and denial of paternity. I encourage you to visit with a local attorney to discuss your rights and obligations as a parent.
If we do not have a written attorney-client agreement: I am not your lawyer; you are not my client; this is not legal advice.