Jhansi is from the Sanskrit-Bundeli — possibly from Jhainsi (reduction of the Bundelkhand region city name). Jhansi is a city in the Bundelkhand region of Uttar Pradesh, India — site of the Jhansi Fort (built 1613), seat of the Maratha rulers. The phrase Jhansi Ki Rani (Queen of Jhansi) is to modern Indian patriotic identity. Subhadra Kumari Chauhan's poem Jhansi Ki Rani (1930) is a work of modern Hindi patriotic poetry — memorized by generations of Indian schoolchildren — with the refrain Khoob ladi mardani woh to Jhansi wali rani thi (She fought valiantly, she was the Queen of Jhansi).
Jhansi does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
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In Pythagorean numerology the letters of Jhansi reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.