I dont know what you should do, or what I would do. But I’m someone who kept my ex husband’s name so it would match my children because he had spread so much bs about me, and ‘othered" me so much as a parent that I didnt want one more hurdle forcing me to ‘prove’ they were mine, with teachers and doctors etc. That wont be a problem for you. But from what you wrote, he sounds dangerous. Maybe you should make it as hard to track her down as possible. I dont know. But that may be what I would do in your shoes.