Since full adoption and using the family name of the adoptive parents are not permissible in Islam, what is the ruling for a newborn child left by his or her unknown mother somewhere and later found by a Muslim couple? Two newborn children were found in this manner at different times, a boy and a girl. Now the girl is 16 and the boy is 19.
Sheikh `Abd al-Rahmân al-`Ajlân, lecturer at the Grand Mosque in Mecca
It is a good deed to be kind to a foundling. These foundlings deserve to be treated nicely. They are not responsible for whatever wrongs their his biological parents have committed.
The girl can even marry the boy if they were not nursed by a common wetnurse. The guardian of the girl in this case will be the ruler. Both the boy and the girl should be treated as non-relatives to the family who took care of them unless a woman of their adoptive family breast-fed either of them. In such a case the relationship will be different, since the rules of fosterage by suckling are similar to the rules of kinship.
Each of the foundlings should be given a distinctive family name to avoid any implication that they came from the same family.
Source: Islam Today
-- Al Arabiya Digital