Legal Question in Family Law in Georgia

She is free to use whatever name she wants. He can't do anything about unless he can prove that she is using it to defraud folks. I doubt that her name just showing up on credit reports rises to this level, unless she did something to make herself identified with his debts.

A husband has no say so as to whether a wife keeps her married name or not. His lawyer would have explained that to him in his divorce.

Your husband is probably not well-informed as to the debts. The only way "her" debts will be on his credit report will be if the debts are joint accounts. The person who will be most familiar with those accounts will be the lawyer who represented him in his divorce, so he may want to check with him. But even if the divorce gave her those debts, he would remain liable to the creditor and his only remedy is versus her.