Can a child's Father's name be charged if a woman is married again?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It is not permissible to change the lineage of the child in a way that he is traced back to other than his father, as this is one of the grave major sins.

Abu Tharr narrated that he heard the Prophet saying: “There is no man (person) who claims to be the son of someone other than his father while knowing that he is not his father, except that he becomes a Kaafir (i.e. he disbelieves), and whoever traces himself back to a people with whom he has no family lineage, then let him await his place in Hellfire.” [Al-Bukhari and Muslim]

The term ‘Kaafir’ in the Hadeeth does not mean that he really becomes a disbeliever, but it is used as a severe deterrence and a stern threat. Another way of understanding this term is that it applies to someone who considers this act to be Islamically lawful.

There are many disadvantages in changing the lineage as it may lead to the mixing of lineage, and thus a person may marry someone who is a Mahram to him while he does not know. This may also lead to losing rights and causing the inheritance not be divided according to the Sharee’ah, so a person who does not deserve something gets it, and the one who deserves it is deprived from it.

For more benefit, please refer to Fataawa 116817, 85803, 86211, 367363, and 154949.

Allah knows best.