Narayani is from the Sanskrit नारायणी (Nārāyaṇī — feminine of Narayana) — from Sanskrit nāra (man/water) + ayana (refuge). Narayani is one of the Sanskrit feminine names — central to traditional Hindu heritage.
Narayani 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 Narayani reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.