Allah says: "Did He not find you an orphan and gave you shelter? And He found you wandering, and He gave you guidance. And He found you in need, and made you independent. Therefore, treat not the orphan with harshness, nor drive away a petitioner (unheard). But the bounties of the Lord - rehearse and proclaim!"
From the above mentioned verse, it is clear that the prophet is being advised to take care of the orphans and raise them with kindness. The prophet is being directed to follow the quality of Allah (kindness) while dealing with the fatherless children. Allah has also discussed the strengths He gave the prophet and he tells the prophet to help the orphan for shelter, guidance and being independent.
However, Islam does not allow a person to change the name of the adopted sons. Zayed bin Haritah was the adopted child of the Hoy Prophet (SAW). When Allah decided for Prophet (SAW) to marry Hazrat Zainab, He gifted these verses to the Holy Prophet so that the prophet may be clear about his biological relation with Zayed Bin Harithah. Quran says, “When Zaid had accomplished his want of her, we gave her to you as a wife, so that there should be no intricacy for the believers about the wives of their adopted sons, when they have accomplished their want of them; and Allah's command shall be performed.”
The above mentioned verse indicates an important thing about the adoption and how it is not a biological relation at all and how the fear of God should be the only motive for such things. He is the most Merciful and expects kindness for the weak and poor. Taking care a child is very noble deed in Islam but does not bound one for the obligations that a biological relation brings as it makes it easy for both; the provider and the orphan, and natural as well.
Below are the 3rd and fourth verses of chapter 33 in holy Quran. Allah says:"Nor has He made your adopted sons your (biological) sons. Such is (only) your (manner of) speech by your mouths. But Allah tells (you) the Truth, and He shows the (right) Way. Call them by (the names of) their fathers; that is just in the sight of Allah. But if you know not their father's (name, call them) your brothers in faith, or your trustees. But there is no blame on you if you make a mistake therein. (What counts is) the intention of your hearts. And Allah is Oft-Returning, Most Merciful."
Muslims should keep in mind that the Islam is the only true religion and everything in the religion is natural and is not based on superficial stories. Allah has made the life easy for us and we should not complicate it for us and others, and must follow the Islam.