Nalini is from the Sanskrit Nalinī. CE Nalini Bhattacharya Indian classical singer.
Nalini 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 Nalini reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.