Paramashiva is one of the trinity of Hindu pantheons, in charge of moksha (layam). Vyasa did not compose sahasranams, but only popularized them through his writings. Note that even before Vyasa many worshipped the Devas with Sahasranamas. All the other sahasranamas are said to have been passed on the writings by Maharishi Vyasa. Lalita Sahasranama is the only sahasranama composed by vagdevatas under Lalita's direction. This has been conveyed to us by the sage Maharishi Vyasa.
At the request of Agasthya, Hayagreeva is said to have taught him the thousand holiest names of Lalita. Agasthya is one of the sages of yore and one of the stars of the constellation Saptarishi (Ursa major). Hayagreeva is an incarnation of Vishnu with the head of a horse who is held to be the storehouse of knowledge. This stotra (hymn of praise) occurs in the Brahmanda Purana (history of the universe) in the chapter of discussion between Hayagreeva and Agasthya. Some of the modes of worship are parayana (Recitations), archana, homa etc. This sahasranama is used in various modes for the worship of the Divine Mother. A principal text of Shakti worshipers, it names her various attributes, and these names are organized in the form of a hymn. This sahasranama is held as a sacred text for the worship of the 'Divine Mother', Lalita, and is used in the worship of Durga, Parvati, Kali, Lakshmi, Saraswati, Bhagavati, etc. An alternative version is that the Upanishad Bramham Mutt at Kanchipuram is where this initiation happened. The temple at Thirumeyachur, near Kumbakonam, is said to be where Agastya was initiated into this sahasranama. The text is a dialogue between Hayagriva (an avatar of Mahavishnu) and sage Agastya. The sahasranama says that 'One can worship Lalitha only if she wishes us to do so'.
These vaag devis are Vasini, Kameshvari, Aruna, Vimala, Jayani, Modini, Sarveshvari, Kaulini.
Lalita sahasranama is said to have been composed by eight vaagdevis (vaag devatas) upon the command of Lalita. Chidagnikunda Sambhuta (one who was born from the altar of the fire of consciousness) and Devakarya Samudyata (one who manifested Herself for fulfilling the objects of the devas) are among other names mentioned in the sahasranama. In verses 2 and 3 of the Sahasranama she is described as a Udayatbhanu Sahasrabha (the one who is as bright as the rays of thousand rising suns), Chaturbahu Samanvita (the one who has four hands) and Ragasvarupa Pashadhya (the one who is the embodiment of love and the one who is holding the rope). Lalita Sahasranama begins by calling the goddess Shri Mata (Revered Mother), Shri Maharagyee (Revered Empress) and Shrimat Simhasaneshwari (The goddess on the lion-throne). The Lalita Sahasranama does not use any such auxiliary conjunctions and is unique in being an enumeration of holy names that meets the metrical, poetical and mystic requirements of a sahasranama by their order throughout the text.
Further, in order to maintain the meter, sahasranamas generally use the artifice of adding words like tu, api, ca, and hi, which are conjunctions that do not necessarily add to the meaning of the name except in cases of interpretation. It is the only sahasranama that does not repeat a single name. The names are organized as hymns ( stotras). Lalita Sahasranamam contains the thousand names of the Hindu mother goddess Lalita.