Kalyani (कल्याणी) is the Sanskrit word for "auspicious" or "that which brings welfare" — used as an epithet of the goddess Parvati. Also a raga in Carnatic classical music.
Kalyani is widely used in India.
Kalyani 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.
In Pythagorean numerology the letters of Kalyani reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.