In NSW there isn't any way that you can change the names on the birth certificate unless you have the permission of both parents. You can hyphenate it or have your DD called by pretty much any name but it isn't official. Most schools now have the ability to record a "real" name and also the "preferred" name.

Also, I am pretty sure that she can't change her name herself until she is 18. But then she can do it without anyone's permission.

Realistically there are heaps of kids that use surnames that aren't what is recorded on their birth certificate.

Good luck with convincing your X.