No idea either but it seems pretty likely (an unusual name).
Yes, that's what bugs me somehow it just 'feels' believable somehow, but on the other hand, see directly above! I've been pretty obsessed with the question for a day or so.
Apparently Nikita is indeed a sister of Shikha and Neha, and has a twin sister who also played at Brown called Nimita!
Not sure there's much evidence of their older sisters' tennis prowess, however...
Wikipedia: Shikha (Uberoi) was born to father Mahesh (who was a table-tennis player for India) and mother Madhu in Mumbai, Maharashtra, India. Her family moved to Princeton, New Jersey when she was an infant. She has one older sister (Diya) and three younger sisters (Neha, Nikita and Nimita). Her four sisters are also tennis players, but of all, Shikha is by far the most successful, and the only one to represent India (the other sisters were born-in represented the United States).