Adoption is forbidden in Islam.
The alternative is that you sponsor an orphan by taking him or her in your custody. That child is not related to you in Islam which means that he is not a son or a daughter to the people who took him in.
This means that he can’t be named after them, he can’t inherit them and he is not mahram to the lady of the house or to her daughters and they must cover from him once he reaches the age of puberty.