If the father of adopted son is not known, he should be called only with his name, he is a Muslim brother. While performing nikah, if he is present in the meeting of nikah and accepts the offer of marriage, there is no need to mention his name with his father’s name. However, if it is needed to mention father somewhere like in nikahnama or passport etc, then in such exigent cases the adopter can mention his name metaphorically in the place of father, but it should be noted that it will be only for paper work, the adopter will neither be his father nor the adopted boy can be his son and legal heir.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband