There is an Indian Name shivAni formed by adding the feminine suffix to shiva. The origin of shiva is probably from a root meaning to grow or swell, and may be related to words for the male generative organ and corpses; though it is usually explained in religious terms from a root meaning to lie down with the implication that everything reposes in shiva. He is mainly (Hinduism is syncretic and often identifies deities of multiple origins) a non-Indoeuropean deity who was associated with welfare, generation, and animals and today is the `destroyer' among the holy trinity in Hindu mythology, and is easily pleased and calm. In its earliest uses the word means auspicious and calm, and those attributes still describe him most closely in current mythology.
His wife (shivani) is durga (difficult to cross), the daughter of Himalaya, and a very loved divine character in Bengal. She is personification of all beneficial power, though when called shivani, one is emphasizing the ascetic and peaceful side.
It would have helped a lot if you had looked at the posting guidelines and followed them. In particular, it is a long time since I had an all uppercase keyboard, and I am not used to reading such text any more. More importantly, you could have specified which ethnicity the name you wanted comes from. Many names have multiple unrelated origins, and you probably are not interested in all possible origins.