Is it permissible to marry off a daughter to an adopted young man who is not yet aware of his adoption, and is it permissible for him to remain registered under the name of the family that adopted him?

If a young man proposing to your daughter is of good character and religious commitment, it is recommended to marry her to him, based on the Prophet's (peace be upon him) saying: "If someone whose religion and character you approve of proposes to you, then marry him. If you do not do so, there will be tribulation on earth and widespread corruption." As for his name, it is obligatory for him to correct his name to align with reality. However, if changing it would lead to harm or difficulties, then it is hoped that there is no sin in him keeping the name, provided he avoids using the name in any legal effect concerning the adoptive family, such as inheritance and mahramiyyah.