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.
The fact that those parents have abandoned their son does not negate the fact that he belongs to them, as he is their son. The adoption which you mentioned does not change anything; rather, the matter must be returned to its original state by attributing the son to his real lineage, i.e. to his father.
Adoption is forbidden as we have clarified in Fataawa 84422 and 82371. It is not permissible for the son to refuse to be bear the father's name as there is a severe threat in regard to a child bearing the name of anyone other than his real father. ‘Ali narrated that the Prophet said: “Whoever bears the name of anyone other than his father, the curse of Allaah is on him, as well as the curse of the angels and all the people; and Allaah will not accept any recompense from him on the Day of Judgment.” [Muslim]
The bad conduct of the parents is not a legitimate reason for bearing someone else's name, so you have to endeavor to reinstate the true lineage of the son pursuant to the Sharee’ah and in order to avoid the mixing of lineages and loss of rights.
In case the court does not accept the annulment of the adoption, then it is obligatory to document the real lineage and have witnesses attest to it in order to avoid the threats that we have mentioned.
Finally, it should be noted that if this child was born out of wedlock, then he bears the name of the mother, and in case of embarrassment, he may take a general attribution, like saying 'son of ‘Abdullaah', or 'son of ‘Abdur-Rahman', without bearing the name of a particular person. For more benefit, please refer to Fatwa 131279.
Allaah Knows best.