By far the most famous commentary on Nammalwar's Thiruvaimozhi is the Eedu, aka the 36000 Padi, which was composed by the Sri Vaishnava Acharya Vadakku Thiruveedhi Pillai, father of Pillai Lokacharya. Now in the introduction to the Eedu, Vadakku Thiruveedhi Pillai discusses the fact that sometimes Vishnu would appear before Nammalwar and other times Nammalwar would suffer pangs of separation from Vishnu:
Thus, he showed unsurpassed devoton to our Lord who has many qualities. To him happiness consisted only in union with Him and grief in separation from Him. And he knew nothing other than Him. Whenever the joy of the experience of the Lord overflowed, he would regard all other things as attaining the Lord and rejoicing like him. He would not even remember that such a contingency as separation was possible; and he would forget even the physiological needs of life. And when the grief of separation overpowered him, he would not remember the joy of union. He would regard all other things as being afflicted with pain, like himself, through separation from the Lord. He would grieve for them also: “Has your heart also been stolen by the Consort of Laksmi?” (11-1). Thus, for him, there is no end to the experience of the joyful and the painful, coming by turns one after the other, and continuing as in the case of Chintayanti endlessly. Therefore, our respected teachers have given the name of Dirgha Chintayanti to our Azhvār.
I’m interested in the part in bold. As I discuss in my question and answer here, when Krishna played his flute to summon all the Gopis for his Rasa Lila dance, there was one Gopi known as Chintayanti who was unable to leave her house and go because her in-laws were watching her. So she sat listening to the music of Krishna's flute, regretting that she could not join him. The blessing of hearing Krishna's flute burnt away all her good Karmas, and the suffering of not being able to go and join Krishna burnt away all her bad Karmas, and she soon gave up her body and attained Moksha.
But my question is, which Sri Vaishnava Acharya gave Nammalwar the name Dirgha Chintayanti? Dirgha means long-lasting, and the name refers to the fact unlike Chintayanti who had this combination of enjoyment and suffering concerning Sriman Narayana for a short time before she departed the Earth, Nammalwar experienced this combination his entire life.
In any case, there were many Sri Vaishnava Acharyas who wrote commentaries on the Thiruvaimozhi before Vadakku Thiruveedhi Pillai’s time, for instance Ramanujacharya’s cousin Thirukurugai Piran Pillan who wrote the 6000 Padi. Did one of them use the name Dirgha Chintayanti?