Shaikh Bin Baz rahimahullah said:
“Adoption is not allowed in Islam. Everyone must be called by his father’s name, whether a male or female. Allah, the Exalted said:
ادعوهم لآبائهم هو أقسط عند الله فإن لم تعلموا آباءهم فإخوانكم في الدين ومواليكم
Call them (adopted sons) by (the names of) their fathers, that is more just with Allah. But if you know not their father’s (names, call them) your brothers in faith and Mawalikum (your freed slaves) [33:5]
Adoption was well-known in Jahiliyyah. Zaid ibn Haaritha was called Zaid ibn Muhammad (may Allah be pleased with him). So when Allah revealed this, he was ascribed to his father. It was said Zaid ibn Haaritha. The Legislation affirmed that it is obligatory for people to be ascribed to their father. It is not allowed to adopt a person. As for raising [a child[, then there is no harm if they raise a child or other than them. And that they are good to him along with ascribing him to his father not to them.There is no harm in that. As for to say the son of so and so and he is not the son of so and so, then this is not allowed at all”.
[Noor ‘ala Darb (23/319)]
Faisal Ibn Abdul Qaadir Ibn Hassan