Bori is from the Hungarian Bori — diminutive of Borbála (Hungarian rendition of Barbara — from the Greek barbaros, foreign). Bori is one of the Hungarian feminine diminutives. Saint Borbála (Saint Barbara, c. 3rd c. CE) was a early Christian virgin martyr — patron saint of miners, artillerymen, and those facing sudden death. across Hungarian Catholic + Eastern Orthodox heritage.
Bori 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 Bori reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.