Is paternity testing necessary if I really believe I’m the father?

No, however; once you have agreed that you are the father in a legally binding way, it is difficult to change. Common ways of agreeing that you are the father are signing a Recognition of Parentage (which is sometimes referred to as a ROPE and is usually singed at the hospital) or admitting that you are the father in a court preceeding that results in a formal order on paternity. A ROPE or an adjudication of paternity gives you the right to seek custody or visitation with the child; it also makes you financially responsible for the child.