Wonderful example of what makes it easy for one to answer: succinct subject line, and providing enough of the information that one knows about it so that one can identify it. (The association with East India in this case is because the whole Radha-Krishna cult was extremely popular there, and, according to some, originated there about a millenium back.)
The root daY meant to divide, allot, posses, destroy, or repent in the Rgvedic use, and is possibly related to the root dA meaning to give (cognate to such words as the latin root of the word dative). In the later language (already by the Atharvaveda), the meaning of sympathize became the dominant usage, and daYA is the common word for sympathy or pity to this day in many Indian languages. In the vedic language, daYA was stressed on the last syllable.
For anvitA, see my earlier response (http://www.behindthename.com/bb/arcview.php?id=527860&board=gen
) to you.
Together, daYAnvitA means someone who is endowed with sympathy, in other words, a compassionate lady. Compassion being a significant part of the divine identity is around in Hindu thought for a long time, but became especially important in the Bhakti movement of East India.