Is it permissible for a girl to supplicate for a non-mahram man, and is it necessary to mention his name in the supplication, and what are the things one can supplicate for him?

It is permissible for a Muslim to ask his Muslim brother for supplication, whether he is a man or a woman, a mahram (definition) (unmarriageable kin) or not. The supplication of a Muslim for his brother in his absence (bi ẓahr al-ghayb) is answered, and an appointed angel says, "Ameen, and to you be the like." There is no harm in supplicating for someone who asks you to do so. It is sufficient to supplicate for them without mentioning their names if you do not know them, such as saying: "O Allah, forgive whoever enjoined me to supplicate." And the supplication should be for the good of both this world and the Hereafter.