Divya Prabandham consists padhigams that are titled Thiruvaimozhi, Thiruviruttam, Peria Thirumozhi, Periyazhvar Thirumozhi, etc What is the basis for this naming convention?

Nalayira Divya prabandham is not a book, it is a compilation.
Swami Desikan had said in Prabandha saram that Nalayira Divya Prabandham is a compilation of twenty-four prabandhams. The Acaryas of our sampradayam has arranged it in such an order.
Twelve Azhvars have graced Prabandhams and they have been compiled under twenty-four titles and twenty-four prabandhams. For instance, the works of Periyazhvar are titled Periyazhvar Thirumozhi and the works of Andal are classified as Thiruppavai and Nachiar Thirumozhi.
Thiruviruttam, Thiruvaimozhi are the titles of the relevant Prabandhams.