Is it permissible for a father to gift a car to one of his sons because he named his newborn after the father, knowing that he did not give gifts to his other married sons who had previously named their newborns after him?

It is legislated for a grandfather to be fair among his grandchildren in giving gifts, just as he is fair among his children. It has been reported from Al-Nawawi, Al-Haytami, and Al-Mardawi — may Allah have mercy on them — that they affirmed that fairness in giving extends to descendants, no matter how distant, even grandchildren.

Therefore, if a grandfather gives a gift to one grandchild to the exclusion of others, it is better to return it because it may cause some resentment among their siblings, especially if the actual beneficiary is the father and not the young child, which implies an impermissible favoritism.