Answer
(Fatwa: 539/D=62/File-D=1433)
(1) The adopted child is not like a real son. The rulings of inheritance and purdah are not for him like a real one. It is also forbidden to write the name of someone else as his father.
(2) The hadith speaks about the virtues which one gets by nourishing a daughter and providing her religious teachings, hence it shall be better. However, you should consider what would be better for you whether a boy or a girl. Or seek the advice of any well wisher who is aware of your situation. No objection would arise if you do not change his/her parent name. However, there is no harm if they just call you mother or father or you say them daughter or son.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband