All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Adoption is forbidden in Islam as Allah Says (what means): {Allah has not made for a man two hearts in his interior. And He has not made your wives whom you declare unlawful your mothers. And he has not made your adopted sons your [true] sons. That is [merely] your saying by your mouths, but Allah says the truth, and He guides to the [right] way. Call them by [the names of] their fathers; it is more just in the sight of Allah. But if you do not know their fathers - then they are [still] your brothers in religion and those entrusted to you.} [Quran 33: 4-5]
So, the people who adopted this woman are considered in the Sharee’ah non-Mahram to her, in a way that she does not mix with their men, or stay in seclusion with them, or expose her ‘Awrah in front of them, …etc. But her husband should not prevent her from visiting them and being kind to them according to the Sharee’ah criteria. But if this could lead to any forbidden acts, then her husband should prevent her from it. If she insists, then you can divorce her, although it is more appropriate to exhort her trying to convince her and showing the Sharee’ah rulings to her.
As for the marriage contract, it is valid provided there is consent of the normal Wali (guardian) of the woman; in this case, it is her father or her closest male relatives from the father's side, like the grandfather. If there is none of these, then the ruler (judge) is her Wali. Now, if you can change the official papers into her real father's name, you should do so; otherwise, Allah does not burden any person more than they could bear. But you should call her by the name of her real father and not the adopted one.
Allah knows best.