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.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer). Do feel free to call me at 404-768-3509 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at email@example.com . An email also does not retain my office, but can help you get an appointment set if you prefer not to call). I am happy to discuss possible representation with you. Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. Note that I am only licensed in Georgia and thus cannot practice in other states. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated Ashman Law Office as a debt relief agency that can help people file bankruptcy.
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.