Can you take the father's name off the birth certificate if the is not the father but is paying child support?

No, you cannot remove his name from the birth certificate without going to court to prove he is not the father. Legally, he is the father and will be responsible for paying child support until the matter is resolved. He can have a DNA test done. He should request one through the court so he can stop paying child support if the child isn't his. It sounds as though you have been playing a game with him and also with your child. You may also have lied on official documents claiming him to be the father. Be fair and have a DNA test taken so you know who the real father is and don't lead this man to believe he is the father when he is not. Your child deserves to know his/her real father.