Yes, if he can establish his paternity legally through a DNA test. Once his paternity is established he can petition for visitation or custody and if the mother retains custody she can request a child support order. A father's parental rights do not depend on the name of the child only on the biological relationship.
A "father" is someone for whom paternity has been established. That done, the father would have the right to pay support and petition for visitation.
If the father wants custody rights, this would be usable in court.
Fathers with parental rights are not always listed on the birth certificate.
Single fathers have no rights in any state see link below
answer is simple. GET A LAWYER
Single fathers have no rights
In the United States, fathers have no rights regarding unborn children. In Kentucky, a father won't have rights to a child unless he's on the birth certificate or until he establishes paternity in court.
DNA testing can be done before or after a birth certificate is signed if there is any question about who the father of a child is or if visitation rights are being contested.
The are not always list yet still have court ordered rights.
A DNA test can prove if the biological father is actually the father. If it is proven he is the father, then he should have all parental rights as any other parent.
The same if he is listed on the birth certificate. NONE
Yes
If you live in the US... The child having the father's last name has NOTHING to do with custody. If Dad is listed on the birth certificate as the father, then both parents have equal custodial rights until a court declares otherwise--you need a custody order. If Dad is not listed on the birth certificate, it will be a simple thing for him to petition the court to establish paternity and once that's done he can then petition for custody/visitation.