Xuanji (玄機) means "mysterious mechanism" — a Daoist term. Yu Xuanji (c. 840-c. 868) was the Tang Dynasty poetess whose brief, brilliant, and turbulent life made her legendary.
Featured in the Quan Tangshi (Complete Tang Poems).
Xuanji 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.
In Pythagorean numerology the letters of Xuanji reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.