The shar‘ī effects of being son or daughter do not apply to the adopted child. The child is not considered his son or daughter.
Question: Are we allowed to adopt children and consider them as our own children?
Answer: It is permissible for a person to adopt a child and taking care of a deserving child is earns the individual reward, but the child is not considered his son or daughter; the child remains a stranger (non-mahram) to him or his wife and he or she does not inherit the person who has adopted him or her. Adoption in the sense to change a child's name and register him in his ID card as his own child is not permissible. It is not permissible to change the child's father name.
1. Ayatollah Seyyed Ali Sistani, Question & Answer, adoption; Ayatollah Seyyed Ali Khamenei, Practical Laws of Islam, Q1007.
2. Ayatollah Seyyed Ali Sistani, Question & Answer, adoption.