Sheikh Sulaymân al-Tuwayjirî
A Muslim may not attribute his adopted children to himself. Allah says: “Call them by the names of their fathers.” [Sûrah al-Ahzâb: 5].
You have to openly declare her father’s real name. If you do not do so, then there is a strong possibility that problems will arise later on.
You have to mention her real name to avoid any the possibility of confusion with regards to her kinship. Such confusion exposes her to the danger of marrying one of her close relatives unknowingly.
You must also mention her real name to avoid the possibility that she should ever be construed as one of your inheritors or that she should ever mix freely as a mahram with your uncles and your sons while she is not.
These are legitimate precautions that you should be aware of.
May Allah guides us all.
Source: Islam Today