You cannot remove the names without the father's consent. Mostly, when the child shares the father's name, the father has the right to know and give the go-ahead to change or remove his name from the child. You must have a lawyer to help you in this process.
vincentA84 is correct even if you were to have another husband and her father allows him to legally adopt her, the biological father's name remains on the birth certificate unless you can prove otherwise that he is not the father,(your daughter may go to court and legally change her name but still may not remove his name from that document.) or she enters the witness protection program-i'm serious! Even if SHE legally divorces him as her father (yes that's a procedure) and a lawyer will have to give you the info on that process, or is emancipated it can't be done. a birth certificate is an official document and only legal measures can change that. she needs a lawyer. you can not be involved in it unless you are acting as agent on her behalf with her consent or if she is too young to sign to that it has to be court ordered. just being her legal guardian may not be enough.
Fathers holding parental responsibility who do not consent to the name change
If the child's father holds parental responsibility for the child, unless he has been absent for a substantial period, his consent will need to be gained before the child's name is changed. Without the father's permission, the only way to ensure that records such as a child's passport are updated into the new name is to obtain an order from the courts. Such an order would give the child's mother permission to go about a legal name change for her child, without the fathers consent. Please read the section below for information on some of the considerations a court will have when deciding whether or not to grant an order, and how to start your application.
If he is on the birth certificate and he is the father why would you want to. You may not like him but absolutely nothing will stop him from being her legal and biological father. If you did that and as an adult she needed proof or a way to contact him or medically get his help and not know his name, because you are unhappy with the guy you allowed to create this baby with would that be fair to the baby? You must have liked him enough at some point I would assume. So you did choose him right? I guess I just don't understand why it wouldn't be enough for you that you just don't associate with him and let the child make their choice later. There are grandparent aunts uncles cousins who's blood is shared by her as well. It's hard for me to understand why someone would do that. Sorry I guess maybe I'm not in touch about this.