Is it permissible for the adopted son (foundling) to keep the name of the father who adopted him, knowing that the latter breastfed the child naturally from his wife, and will inform him of the truth of his lineage when he reaches understanding, and he has enough wealth to bequeath to him an amount that would enable him to inherit as one of his own children, in addition to the father's fear for him of people's talk should they learn of his true lineage?

If there are five full and satisfying breastfeeds, your wife becomes the child's wet nurse (foster mother), and you become his foster father. Your children become his foster siblings. However, fosterage does not establish the legal rulings of filiation (sonship) in inheritance; it only establishes mahramiyyah (prohibition of marriage).

It is not permissible to attribute the child to you as a son, even if he becomes your son through fosterage, in order to avoid the semblance of adoption, which is forbidden in Islamic law. Excuses do not validate this. If it is not possible to cancel his attribution to you, then necessary precautions must be taken to prevent the mixing of lineages and the loss of rights. Full reward is hoped for guardianship and showing kindness to him.

It is permissible to make a bequest to the child within the limits of one-third of the inheritance or less. As for anything exceeding one-third, it is not executed except with the permission of the heirs.