A legal name change involves going through court. We have no way of predicting if the mother would lie to a court, but if your spouse's address is on record for child support purposes it would be pretty implausible for her to try to get substituted service based on not knowing his address.

What the kids call themselves for unofficial purposes? That's something your husband can consider addressing through the custody court, if it's a problem and is of sufficient import to him to take that step.