You'd hope that the prison might contact the next of kin if someone in it died.
Still, three months might not be too unreasonable if the DOC can show that it was making efforts. It's possible that the inmate did not give a proper name or address for next of kin (I assume they are asked when processed) or gave a wrong address. In such a case there might be difficulties locating family. It might take three months if you didn't know where to start looking.
Of course, those who visited him and/or sent him letters and had the same last name might be people you'd check pretty quickly . . .
Thanks to FMF.