Hayagriva teaches Agastya everything about Lalita but her thousand names, and waits to be asked; the names were made by the goddesses of speech at her command and first sung before an assembly of all the worlds. Tirumeeyachur says she made them after the war, when her anger cooled.
Lalita Sahasranama, opening chapter, with Lalitopakhyana 5
Pan-IndiaShakta
Agastya, worried for people lost in ignorance, reaches Kanchi and worships Ekamra and Kamakshi; Vishnu appears as Hayagriva, teaches that release lies in worshipping Tripura, and leaves Hayagriva as his teacher. Hayagriva teaches the history of Lalita, Shripura, the fifteen-syllable mantra, the rites and hymns and the thousand names of Mantrini and Dandini. Agastya asks why Lalita's own were left out. Hayagriva, delighted, says they are secret, to be given to the devoted and never to the faithless. Lalita had told the goddesses of speech, Vashini and the others, to compose her thousand names; they sang them before crores of Brahmas, Vishnus and Rudras and all the Shaktis; she told the gods to recite them and teach them to her devotees.
South India · Tirumeeyachur, near Peralam, Tiruvarur district, Tamil NaduFolk
After killing Bhanda the Goddess stays furious; Shiva asks her to take the name Manonmani and do penance on earth; at Tirumeeyachur she grows gentle and makes the goddesses of speech praise her with a thousand names, beginning Shri Mata. Hayagriva sends Agastya to where she is Manonmani; Agastya and Lopamudra chant the names; she shows herself as the nine gems; Agastya sings the Lalitha Navaratna Mala. She sits on the Shri Chakra throne, right leg folded over left; pirandai rice is offered on a lotus leaf.
What is different here:
Adds why the names were made (her anger after the war), the place, Lopamudra and the nine gems.
Sources: Lalita Sahasranama with Bhaskararaya's commentary, tr. R. Ananthakrishna Sastry (2nd ed. 1925, archive.org); Lalitopakhyana ch. 5, Agastya's pilgrimage and the manifestation of Vishnu, tr. G. V. Tagare (wisdomlib); Sri Lalithambigai (Meghanathar) temple, Tirumeeyachur (Dinamalar temple guide); Tirumeeyachur Lalithambika temple sthala puranam (Thanjavur Parampara); Tirumeeyachur Mehanadhar Temple (Wikipedia)