Is it permissible for a slave to inherit from his master and be attributed to him, with his identity changed in official documents? And how should this situation be handled if it is not Islamically permissible?

If you claim that those you call your cousins are in fact the children of your grandfather's slave, then this claim requires the establishment of lawful proof if they deny it, because people are entrusted with their lineages.

If it is proven that they are the children of your grandfather's slave, then the ruling is divided into two issues:

Firstly: The ruling on your grandfather's bequest to his slave: If he was a free man at the time of the bequest: It is a bequest to a free person who is not an heir, and it is valid within the limits of one-third. Anything exceeding one-third is not valid unless the heirs consent. If he was a slave at the time of the bequest: Bequest of a common share of his wealth (e.g., one-third): The Hanafis, Hanbalis, and one opinion among the Shafi'is held it to be valid, and it is used for the slave's manumission. If the slave is freed through the bequest, he is emancipated and is entitled to the remainder of it. Bequest of a specific item (e.g., a garment or a house): The majority hold it to be invalid because the slave is the property of the heirs, making it as if it were a bequest to the heirs. However, Malik, Abu Thawr, and one narration from Ahmad said it is valid.

Secondly: The ruling on their lineage to your grandfather: It is not permissible for a slave to attribute himself to his master (your grandfather) instead of his real father, due to the Prophet's (peace be upon him) prohibition of attributing oneself to other than one's father, considering it one of the greatest fabrications, and that Paradise is forbidden for whoever claims a father other than his own while knowing it.

How you should act now: You must advise them to attribute themselves to their real father and to change the official documents that attribute them to other than their father.