She could try an end run around the law, but if/when you found out you could have the order changing the name overturned/vacated or whatever the legal term is. As long as you are actively involved with your child and her schooling I doubt this could happen without your knowledge.
Some people compromise and go to a hyphenated version of the name, but I don't really agree with that either. If she hyphenates to yourname-hermaiden and she remarries, then your child has a name neither parent has(assuming ex changes her name again) and has to change again? Or what if your child hyphenates to stepdads-yours and they divorce and then she has to change AGAIN.
IMO the name the child is born with should be theirs for their life. If the child is so young that they are unaware of their last name, I could be convinced to go for some sort of change. Otherwise they shouldn't have to change it until they are adults and choose to. If the parents don't make an issue out of it, it likely won't matter.