Adoption in the sense of changing one’s identity and lineage for a false lineage is prohibited in Islam; but at the same time, it is allowed for Muslims to adopt a child in the sense of taking him/her under his/her wing for providing both physical and spiritual care for him/her. The Prophet (peace and blessings be upon him) said, “The best house of Muslims is one where an orphan is cared for.”
Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, states: “There is a great blessing and reward in taking care of orphans. In the Qur’an the Believers are urged again and again to take care of the orphans. The Prophet (peace and blessings be upon him) is reported to have said, “I and the guardian of an orphan will be in Paradise or Jannah like these two fingers and he joined his two fingers.” (Reported by al-Bukhari)
In another Hadith he mentioned that “when a person puts his hand of compassion on the head of an orphan, for every hair of that orphan he will receive a blessing from Allah.” (Reported by Ahmad)
Therefore, I strongly recommend that muslims should take care of the orphans. As far as adoption is concerned, I can say that according to the Shari`ah, it is not allowed to deprive a child of his/her biological parents’ name. You can keep the child, provide him/her good home and take good care of him, but do not give him/her your last name. Allah says in the Qur’an, “He (Allah) has not made your adopted sons as your sons. Such is only your speech by your mouths. But Allah tells you the truth and He shows you the right way. Call them by the names of their fathers, that is more just in the sight of Allah. But if you do not know their fathers’ names, call them your brothers in faith or your friends. There is no blame on you in whatever mistakes you made in this matter, but what counts is the intention of your hearts. Allah is oft-Forgiving and most Merciful.” (Al-Ahzab: 4-5)
In America for the purpose of tax-exemptions, health insurance, school admissions etc. you may need to give the adopted child your last names. Such names can be provided with a clear understanding that you are only the guardians. The orphan children should be told about the names of their real parents. In your own home you and your children should be aware of this fact that these children are not your biological children, and you are not their biological parents.
It stands to reason that when those orphans grow up then they will not be mahram (unmarriageable) to you, to your spouse and to your own sons and daughters. They will also not inherit anything from your property unless you give them something as a special gift through the provision of will.”