Is there a Sanskrit name or term for the "Star of David" itself, since archeological evidence shows it being part of Vedic culture in India?
There is no word in Sanskrit for star of David. Intertwining triangles are part of yantras. Wikipedia has a general descriptive page on yantras. Downward pointing triangles are symbols of the female, yoni or shakti element; and upward pointing triangles are symbolic of the male, lingum or vahni (fire) or shiva element. Thus the intertwining of the two is the intertwining of the male and female principles, Nirguna and Saguna Brahman, Shiva and Shakti, the Yin and the Yang, the positive and the negative. The two opposites always interacting with one another. The one appearing as two.
In the Greek lexicon, the Greek letter 'Delta' which is and upward pointing triangle, symbolized the female.
See Myths and Symbols in Indian Art and Civilization by Heinrich Zimmer pp 147-8.