Well, I'm certainly no expert with regard to this, Mommyofjom. But my thinking would be that the kids should be able to choose for themselves what last name they want to have. It's simply important for them to understand, to the extent that they can, they can't go back-&-forth. They can make one change. And, perhaps, they can even change back one time, if they decide they've made a mistake. But they can't just be flip-flopping back-&-forth since changing one's name is a legal proceeding & presumably there is some expense involved.
Perhaps there will be some other members, here on PC, who will be able to speak with more authority on this subject. Good luck!