Azumi is from the Japanese a (安 — safe, peaceful) + zumi/sumi (純 — purity / 澄 — clear) or a (亜) + zu (寿 — longevity) + mi (美 — beauty). Princess Azumi — Japanese heritage naming.
Azumi 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 Azumi reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.