What is the ruling regarding a child born out of an illegitimate relationship, and is it permissible to acknowledge him as a son and give him the father's name?

The majority of scholars hold that the child of zina (fornication/adultery) is not attributed to his biological father from zina and does not inherit from him. Rather, he is attributed to his mother and her family. All legal rulings of sonship, such as mahramiyyah (being an unmarriageable kin), guardianship, 'asabah (agnatic kinship), and inheritance, are established for him through his mother.