Can a father give up his rights and still pay child support?

How can I get a man's name off my child birth certificate who falsely put his name on it?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

But I'm surprised you asked since the thread you posted in contained the answer.

First, you start with a false assumption that a father can give up his rights. Only a court can terminate rights and courts will not issue a TPR to allow a parent out of paying support.

But IF a father's rights are terminated then it depends on local laws whether support stops or not.

How can i get a man's name off my child birth certificate who falsely put his name on it?

It willl depend on the local area and the law there. He is the legal father with all rights till then. Are you the mother, the man who thinks he is the real father?

I've merged both your questions. You need to be more detailed in your questions. Please post any followups as answer to this thread.