A name change is just a court order that gives her a new name, nothing else. It does nothing to change the relationship between your husband and your daughter. You should consider a step parent adoption. Not only does your husband become the legal father, and her name is changed to his, but you get a new birth certificate with the father's name on it.
I am exclusively a family law attorney, practicing primarily in the metro Atlanta, Georgia trial courts. However, I handle appeals from anywhere in Georgia.
A name change will change her name, but won't add the father to the birth certificate. A step-parent adoption would do both, and may be a better option. If the child is very young, the child won't likely ever know. If the child is older, she may know. In any event, to give you good advice in this case I'd want more details. Feel free to call me at 404-768-3509.
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So long as your daughter is still a minor and you are the sole legal parent (i.e., biological father never legitimated), you have no obligation to notify him or her about the name change. The process is fairly straightforward and involves simply filing a petition and draft Order with your local Superior Court and awaiting a hearing date. If no objection is interposed, the petition should be summarily granted. However, as my colleagues above note, the name change alone would not make your husband the child's legal father, and it would not place him on her birth certificate. I recommend you contact a local attorney to discuss the best course of action for you and your family.