Mizuki is a Japanese name written 美月 — combining 美 (beautiful) and 月 (moon). Other kanji combinations are possible: 水希 ("water hope"), 瑞希 ("auspicious hope").
Mizuki has been among the most popular girl's names in Japan since the 1990s.
Mizuki 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 Mizuki reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.