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Need to see it in a Brahmi derived script to be sure, because I have not heard it; but there is a possible onomatopoeic root shinj/sinj (with a palatal n, and either a palatal sh or a dental s) meaning to make a shrill cry/roar, tinkle, rattle, jingle, and a bunch of other such things. It is a very old root (goes back to the vedic period), but still in some use in poetry to mean the tinkling of metallic ornaments, e.g., bells in an anklet. Words from poetry, if they sound nice, often become names in some communities in India.

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shinjita/sinjita/shinjitA/sinjitA (the forms with the open -A are feminine) means tinkled/tinkling/sounding etc.