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There is little reason to think of Hitisha as arising from combining a Hindi word (from Sanskrit hita with an Arabic word not used in Hindi. The Isha in the word most likely refers to the Hindi word Ish (from Sanskrit Isha) meaning master, and is patterned after a lot of names ending in that name element. The element -A at the end is probably the feminine suffix.

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In Sanskrit, the compound would have been hiteshA, but this is a new coinage. There are other words ending in -ishA (often coming from the desiderative suffix in Sanskrit) that might have made it a nice sounding name.