Sutra:
81. piRarkkuriyanAnavanRu than vailakshaNyaththaik kAtti meetkalAm; thanakkennumanRu yOgyathaiyum kooda azhiyum.

Meaning:
If a person becomes enslaved to another then it is possible to shown him the difference between others and the Lord and correct him. If he is enslaved only to himself (living as I and mine), it is difficult to bring him to the right path (therefore, it can be taken that removal of anya sEshatvam is connected to the removal of svasEshatvam, which is shown by the nama:).

Sri PBA Swami's Sarartha Deepikai:
Previously it was told that the nama: explains the ukAram. Also, that the ukAram removes being enslaved to others (other than Him) which includes the removal of being enslaved to oneself. If the nama: explains the ukAram, then can it stop at stating that one does not belong to one's self? Should it also not show that one does not belong to others?

Between anya sEshatvam and svasEshatvam, it is svasEshatvam that is more dangerous. If a person is enslaved to another, it means that the person is agreeable to that idea; then it is easy for Him to show this person His divine qualities and the difference between Him and others and enslave him. When a person becomes enslaved to himself, it is difficult to correct him and make him enslaved to the Lord.

Therefore, as svasEshatva nivrutti is more important than anya sEshatva nivrutti, it is that which is shown in the nama: part.