Peri means a fairy — a lovely, delicate spirit of Persian and Turkish myth. It carries enchantment and grace.
Peri 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 Peri reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.