Why this order and what do these names signify ?
This is explained by Sri Parasara Battar (Battar is Koorathazhwar’s son. Koorathazhwar is Ramanujar’s shishyan who was key behind Ramanujar writing Sri Bhasyam the commentary on Brahmasutra). There are various reasons for the order of the names. If you look deep into it we will understand the reason for the order of the names. The bhasyam of Vishnusahasranamam by Parasara Battar - BHAGAVAD GUNA DARPANAM explains the reason behind this order in detail. The organization and structure in the composition refers to the guNas of the Lord Sriman Narayana in the five manifestations in which He has revealed Himself to us, as described in the PancharAtra Agamas.
These manifestations are:
4. archa, and