The reply depends on what you mean by adoption. If you mean looking after and bringing up a child, then it is great deed of reward. The Hadeeth says: Best of the homes is a home where an orphan lives with honor. Also it is narrated from the Prophet Muhammad (SAWA): I and orphan sponsor are in the Paradise together.
But if you mean to look after the child and deprive him from the name of his real father , mother and original family, then it is unlawful in Islam to deprive the child from the name of his father, mother and original family.
Allah says in Quran (Call them by their fathers' name)(ادعوهم لابائهم)Al-Ahzaab,5.
Also it is not allowed to deprive the child from his real mother (إن أمهاتهم إلا اللائي ولدنهم )(Their mothers really are who gave birth to them) Al-Mujadalah ;2.
Claiming the adopted child as a real son or daughter is forbidden in Quran (وما جعل أدعياءكم أبناءكم ذلك قولكم بأفواهكم ) (Allah did not make your sponsored/ adopted/ fostered children as your children, that is what you say in your mouths).
So, it is very good to adopt a needy child with keeping his father's, mother's and family name with him always.