All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Changing the name of the child or that of his mother is permissible especially if the meaning of the original names is bad, in which case it is recommended to change them, and it might even be an obligation to change them according to their meaning. For more benefit, please refer to Fataawa 88621 and 81226.
However, it is not permissible for this man to attribute this child to his name as he is not his real child, because this is adopting him, which is forbidden. Attributing the child to him does not lead to any religious implications [i.e. does not render the child an heir or a Mahram (i.e. a person whom one is permanently prohibited from marrying due to suckling, marital, or blood relations) and so forth]; for more benefit, please refer to Fatwa 84422.