From what I remember Islam is generally against adoption except orphans and even then they retain their biological father's name.
The child is an extension of his father and the bearer of his characteristics. During his lifetime he is the joy of his father's eyes. While after his father's death the child represents a continuation of his existence and an embodiment of his immorality. The child inherits his features and stature as well as his mental qualities and traits, both the good and the bad, the beautiful as well as the ugly. The child is a part of the father's heart and a piece of his body. These facts cannot be altered by adoption of that child by anyone and Islam has provided the inalienable right of the child to his lineage as well as that of the natural father to lineage.
Also, it seems that adoption was discouraged after Old Mo saw his adopted son's wife and took a fancy to her therefore he had to request his adopted son (Zaid, I think it was) to divorce her so that he could marry her and due to this inconvenience he (or Allah) made adoption illegal in Islam.... how convenient.
Before the advent of Islam, that is, before he received the call to prophethood, Prophet Muhammad (peace be upon him) had him- self adopted Zaid bin Harithah, who had been captured as a child during one of the raids on his tribe which were common occurrences during the period of jahiliyyah. Hakim bin Hizam had bought him for his aunt Khadijah, and after her marriage to the Prophet (sallallahu alaiyhi wassallam), Khadijah presented Zaid to him. When Zaid's father and uncle learned his place of residence, they came to the Prophet (sallallahu alaiyhi wassallam) to demand Zaid's return. The Prophet (sallallahu alaiyhi wassallam) gave Zaid a choice, and he chose to stay with the Prophet (sallallahu alaiyhi wassallam) in preference to his father and uncle. The Prophet (sallallahu alaiyhi wassallam) then set him free and adopted him as his son in the presence of others. He was thereafter called Zaid ibn Muhammad (son of Muhammad) and became the first of the freed slaves to accept Islam. Allah wished that this relationship that is, adoption, be discontinued.
Later on, Zaid married the Prophet's cousin, Zainab bint Zahsh. Zaid and Zainab were not happy together, and Zaid became increasingly dissatisfied with his wife, complaining frequently to Prophet Muhammad (sallallahu alaiyhi wassallam). The Prophet (sallallahu alaiyhi wassallam) knew, through divine revelation, that Zaid would divorce Zainab and that he would afterwards marry her himself Thus, whenever Zaid complained to him about his wife, the Prophet (sallallahu alaiyhi wassallam) would tell him, "Hold on to your wife and fear Allah." At that point Allah revealed some verses of the Qur'an (33:37) admonishing the Prophet (sallallahu alaiyhi wassallam) and at the same time fortifying his will to face society in demolishing the remnants of this ancient system, in this case, the established practice which prohibited a man from marrying the ex-wife of a stranger who had been adopted as a son. The Qur'an goes on to support the Prophet (sallallahu alaiyhi wassallam) in this action, confirming its lawfulness and re- moving any stigma attached to it.
Here's the full article on adoption in Islam:
http://worldupdates.tripod.com/newupdates10/id66.htm
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