Is the Shringeri Sharadamba - Goddess Saraswathi or Goddess Lakshmi or Goddess Parvathi? Since they can attribute the names of different Goddesses to one single Goddess & there are similar references for various Gods being converged into one God?

 I do not know about Sharadamba.

In Southern Peninsula and in South East Asian countries, Lord Murugan is worshipped with two consorts- Deivayani and Valli.

Goddess Deivayani is from Shringeri. Today also, the priests of Deivayani temple in Kataragama, Sri Lanka are descendants from Shringeri.

Mohan N R's answer to Why did Lord Murugan marry Valli and Deivanai both? What is the philosophy behind this story?

Another consort Vedda Valli is the daughter of the native.

Devyani is considered as “Energy of Action”.

Valli is considered as “Energy of Desire”.