All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
As regards that woman, she is very sinful and she must repent. For details, please refer to Fatwa 86527.
Your marriage to her is void according to the consensus of the scholars; please refer to Fataawa 87134 and 120395. Hence, you must separate from her immediately and you are not permitted to have sexual intercourse with her.
Regarding whose name the child bears, please refer to Fatwa 90732 for a detailed explanation.
It is not permissible for her husband to have sexual intercourse with her until after he makes sure that she is not pregnant by you. This can be done by her having one menstrual period according to the view of some scholars.
Allaah Knows best.