Anyone have experience with changing a minors name?

So long story short my husband has a court order stating that his childs last name be changed to have his and exes name hyphenated (like Jones-Smith). He also has a court order stating that his name is to be added to the childs birth certificate. Will the court take care of this, is this something he can do on his own, or will him and his childs mother go together to do this?