How do I have my name put on my daughter's birth certificate? Paternity was acknowledged at her time of birth, the mother and I were never legally married, my daughter does have my last name yet on birth certificate, yet it states 'Information not Entered'. I do not understand how it can state that after I already acknowledged paternity in hospital. I've been paying child support for the last five years with regular visitation. The mother is refusing to go with me to a state office building to have my name added. What do I do?

I don't know if that is common for the state to not put your name on the birth certificate right off the bat. IF it is not common then I would say she pulled something to not include your name especially when she is refusing to cooperate with you to get it added. You say paternity was acknowledged at time of birth. That doesn't sound like a paternity test. My suspicion is you should file with the child support court for a paternity test.
I may be way off on this but it seems to add up.

Acknowlege of paternity and the mother listing your name on the birth certificate and you signing the birth certificate at least in the states I know are two separate things. You will have to file a petition ( not sure if that is family or probate court or another court in your state) to have the name added. So basically you will need an attorney. If the mother does not object it should be easy, but if she objects I am not sure you can force them to change the child's name. But they may add you to the birth certificate.