Your daughter’s last name is apparently the same as her father’s. That her father’s last name is the name of his adoptive father rather than his biological father isn’t important here. The basic rule is that for a name change of a minor both parents generally must agree to the change. If he will not agree then it is likely the name change will not be approved. See the following information from Michigan legal aid for more information:
http://michiganlegalhelp.org/self-he...or-childs-name