Information sought through a comment: May I ask what is the source of this interpretation of Vāmakeśvarī? I would be interested to know if you have come across an interpretation of the name Vāmakeśvarī or Vāmakeśvara elsewhere?
Clarification to the best of my ability: There are two namas in Lalitha Sahasranamam beginning with Vamakesha. The first one is nama 351. Vāmakeśi and the other one is nama 945. Vāmakeśvari. Apart from what was discussed in nama 351, I have only the following additional information.
Vāma has innumerable meanings such as beautiful, splendid, Shiva, Durga, Lakshmi, Sarasvati, a beautiful woman, wife, left side, etc. Keśi means hair. Then nama 351 means She has beautiful hair. Bu this interpretation does not go with the preceding and succeeding namas. Nama 350 refers to Goddess Sarasvati and nama 352 could mean Durga. If these interpretations are correct, nama 351 should refer to Goddess Lakshmi, which seems to be appropriate.
Nama 945 is Vāmakeśvari which refers to Vamakeshvara tantra. This tantra is said to be the 65th tantra apart from the 64 discussed in Soundarya Lahari verse 31 and nama 236 of this Sahasranamam. Vamakeshvara Tantra is said to be the most important tantra for Sri Vidya worship. This tantra discusses on internal worship of Shakthi. Vamakeshvari is said to be the source of this Universe.
Shakthi asks Shiva in Vāmakeśvara tantra “Lord, you revealed to me all the 64 tantras. But you have not told me about 16 Vidyas.” Shiva answers by saying that this has not been declared yet and that it is hidden so far. Then Shiva begins declaring this tantra to Devi. Everything in this tantra has been revealed in a very subtle manner.
For example the bija ‘hrīm’ is declared as ‘the form of vidya protecting the self is Shiva, Agni, Maya and bindu.’ Unless one knows the bijas of these gods/goddesses, it is difficult to make out the hidden bija. Shiva bija is ‘ha’, Agni bija is ‘ra’, maya bija (root of ‘eem’ or kamakala) is ‘ī’ and bindu is the dot. By joining all this, the bija ‘hrīm’ is arrived. Shiva declares a number of uncommon yet powerful bijas in this tantra.
Vāmās mean those who worship Her through left hands. They do not follow the five principle yajnas that will be discussed in nama 946 subsequently. She is the Goddess for these left hand worshippers. She is also known as Vāmeśvarī, which refers to Her divine power which projects the universe out of Shiva (the Brahman without attributes) and produces the reverse (vāmā) consciousness of difference.
Vamadeva is the back face of Shiva.