The name Greek Library is obviously fictitious and was created to distinguish this building from the nearby Latin Library (n. 15).
The two buildings were named Libraries in the sixteenth century by Pirro Ligorio, whi thought that the rectangular niches could contain papyri and manuscripts. He called them them "Greek" and "Latin" simply because they were two.
Actually in some niches there are doors and in any case there are no traces of shelves.
According to Filippo Coarelli, the Libraries could be two summer triclinia, because they were oriented towards the north. But this is not very likely, since there is no place for a stibadium, which was found instead in all the other triclinia identified in the Villa.
Finally, according to Kähler, the Libraries resemble the Vitruvian turres of the Villas, and this is perhaps the most convincing idea.
The two Libraries probably were two monumental atria decorated with statues, a sort of Propylaea, which marked the access to the private quarters of the Villa for those coming from the north. An imposing building, a symbol of imperial luxury and wealth.
Given that the heating systems in non-thermal buildings exist only in very few ones of the Villa, it is likely that the Greek Library was used by the emperor as a winter residence before the construction of the Winter Palace (n. 33), which similarly had a heating system for winter.