What is the ruling of Islamic law regarding the marriage of a man to a woman who is registered under her grandfather's name in the civil registry, despite her knowing her biological parents, and is this marriage considered Islamically permissible?

If your wife's grandmother's husband is her father's father, then it is permissible to register her in his civil record, because he is considered her father, legally and customarily. However, if he is not her father's father, then it is not permissible to register her in his record, to prevent the mixing of lineages. The wife must be attributed to her real father, based on the Prophet's (peace be upon him) saying: "Whoever attributes himself to other than his father, or pledges loyalty to other than his masters, upon him is the curse of Allah, the angels, and all of mankind." And his saying: "Whoever claims to be the son of someone other than his father, while knowing it, Paradise is forbidden for him." As for the marriage contract, as long as it has fulfilled its conditions and pillars and its impediments are absent, it is valid and is not affected by what happened.