What is the ruling on writing "Endowment for the sake of Allah the Almighty as a reward for so-and-so, son of so-and-so" on copies of the Qur'an obtained for free from the Ministry of Endowments and affixed to their first page?

As long as you obtained these copies of the Qur’an through legitimate means, there is no objection to endowing them to the mosque or elsewhere as a reward for your father or others. There is also no objection to writing or attaching the name to them, provided that it is free from boasting and the person is safe from showing off. However, it is preferable not to write on them, as that is closer to sincerity, and because concealing charity is better than disclosing it unless there is a necessity, as Allah the Almighty said: "If you disclose your charitable expenditures, they are good; but if you conceal them and give them to the poor, it is better for you, and He will remove from you some of your evil deeds. And Allah is acquainted with what you do."