Can a couple raise an abandoned child and give him their family name, knowing that he will be registered in the civil registry with the family name only, without mentioning "son of so-and-so," because he has no known lineage?

Raising foundlings is a good deed and a great act of obedience. However, it is not permissible for the person caring for the foundling to attribute the child to themselves, as this is forbidden and leads to the mixing of lineages and the loss of rights. Allah Almighty says: "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 your brothers in religion and your allies." A good name should be chosen for the child, such as Abdullah or Abdul Rahman. Attributing the child to the family without a specific person is not permissible, for fear of future complications. When the child reaches adolescence, he becomes a non-mahram to the women of the household, and it is not permissible for him to be alone with them unless one of them breastfed him five full feedings during the first two years of his life, in which case he becomes her son through suckling.