What is the ruling of Islamic law regarding a father registering his trucks in the name of his female cousin's son instead of his own male children?

There is no blame upon your father for registering cars in the name of whomever he wishes. If he intended a gift (hiba), then it should be examined whether it occurred during a life-threatening illness or not, and whether possession was transferred or not. If he intended a bequest (wasiyya), then it is permissible within the limits of one-third (of the estate). However, if he intended another permissible purpose besides a gift or a bequest, then there is no blame, provided that measures are taken to safeguard the rights of the heirs.