Rauni is from the Finnish Rauni — Finnish mythological deity name (possibly from Proto-Germanic Raunaz). Rauni is one of the Finnish feminine names — central to traditional Finnish Indigenous Finno-Ugric heritage. Finnish feminine name.
Rauni 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 Rauni reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.