Salaam Alailukn, Sir, can a mosque, well, or orphanage be made on other's name or on their behalf like parents, brothers etc. Is it also true that the reward (if made on their respected names) of constructing these wells or mosque will be entirely delivered to those on whom they were named. And will one who constructed on their behalfs also rewarded? Thank you.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

If by your statement "a mosque, well or orphanage be made on other’s name" you mean that the one who informs about it says that the one who built it is other than the one who really built it, then this is a lie and not permissible because it is telling something contrary to the truth.

However, if you just mean naming the mosque or the well like saying the ‘mosque of so and so’ or ‘the well of so and so’ then, in this case, one should look to the condition of the endower; if he conditions naming it with a particular name, then it is not permissible to oppose him about it, because the jurists mentioned that everything that is related to the Waqf (endowment) one should refer it to the condition of the endower. If the endower did not condition a particular name, then it is the one who is running it [who is taking care of the Waqf] who should name it. In any case, the reward will be for the one who built it or participated in building it.

Again, if you are inquiring whether or not it is permissible to donate the reward of building it (the Waqf) to another person, then the answer is yes, and every act of getting closer to Allaah which a Muslim does and donates its reward to another Muslim whether he is alive or dead, then Allaah will make him [the one to whom it is donated] benefit from it, Allaah willing.

However, it is better not to put a sign with the name of the donator or the name of the person to whom it is donated because it is better to conceal the charity rather than to show it as Allaah Says (what means): {… 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,…}[Quran 2:271]

Ibn Katheer said: “This is evidence that concealing a charity is better than showing it, as this is avoiding showing off, unless there is a preponderant benefit in showing it, like making people imitate him (the giver), then this is better in this case, and the Prophet said: “The one who recites the Quran loudly is like the one who donates openly [showing his charity], and the one who recites the Quran silently, is like the one who donates secretly.” In principle, concealing a charity is better for the above verse.”

To sum up, there is no need to write the name of the person who endows something, because it is Allaah who gives the reward and He Knows the intention of the donator and the one to whom it is donated.

Allaah Knows best.