Sorry it wasn't more specific. I looked up the statutes as well, but believe it or not they're even less informative. (They're
here, Sec.
527.270,
527.280,
527.290.)
The court rules indicate that you can initiate a name change for a minor by consent, or do it with notice to the other parent if you don't have consent. Generally speaking, in a dispute between parents a court evaluates a contested petition by applying the "best interest" standards - is it in the child's best interest to have the new surname. I suspect that, given the facts you describe, even if the father tries to dispute the petition the judge will grant the name change.