Mayuri is from the Sanskrit मयूरी (Mayūrī — peahen, peacock-female) — feminine of mayūra (peacock). Mayuri is one of the Sanskrit feminine names — central to traditional Hindu + Buddhist heritage.
Mayuri 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 Mayuri reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.