Even if DF doesnt appear on bubs birth certificate it wont be questioned by anyone (eg Centrelink)?
Due to him not being bio dad, he doesnt wish to be named on certificate
I'm confused.... he wants to give the baby his name, just not officially? Are you going to be claiming child support from the baby's biological father?

According to the law (from CSA website):

... a person is the child’s biological father if:
-the person is named as the father on the birth certificate or adoption certificate
-the person signs a statutory declaration (a legal document) saying he is the father
-the children were born during the marriage
-the children were born within 44 to 20 weeks of a period of living together [emphasis added]
-the court makes an order or finding that a person is the children’s father or a person who is liable to pay child support.