Praise be to Allah.Praise be to Allaah.
It was reported in a saheeh hadeeth that the child belongs to the bed and the stone is for the adulterer, so it is not permissible for the child to be given the name of the adulterer or of the mothers husband. Rather, she should be called after her mother, so that her name will be So and so the daughter of So and so [her mother]. Otherwise, her guardian should choose for her a common name that cannot be attributed to any specific person. For the girl who is asking this question, there is no sin on her at all because of her parents sin, and if she is patient in putting up with any annoyance as a result of it, she will be rewarded for that, in sha Allaah. And Allaah knows best. See also Questions # 6195.