Answer
(Fatwa: 1158/909/D=1431)
According to Shariah, adoption does not make a child real son. In Islam, the practice of adoption (declaring someone as son) is ineffective. Therefore, according to Shariah, it is not right to write your name instead of his father’s. It is forbidden and sin to attribute someone to other than his father, also he will not be declared your heir due to adoption islamically. When he is your nephew, then after he attains puberty, it will be wajib on your wife (if she has not breastfed him) and your daughters to observe purdah before him. According to Islam, he will be your nephew. If you want to gift him, something then you can do it by giving it into his possession or you can make a will (up to one third of your property) after your death.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband