The biological father would have to give his consent for your husband to adopt your daughter. Same goes for changing her last name - that would have to be done through the court system and the biological father would have to be notified of the proceeding and he would have the right to appear and object.
Your husband cannot adopt and you cannot change your child's name unless her biological father consents.
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Before your daughter could be adopted there would have to be a termination of the biological father's parental rights. The termination would mean he has no right to custody or visitation and no obligation to support the child. If the biological father agrees to the termination, then it is relatively straightforward to have a step-parent adoption. If he does not agree, you would have the burden of proof as to why his rights should be terminated - and it is a very high burden.
He would also have to consent to the name change.
Husband can not adopt unless the biological father's parental rights are terminated. If he has supervised visitation, then he still has parental rights. Make sure you receive child support from him, his rights goes along with parental obligations. Child support is dues until his parental rights are terminated.
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