Turandot is from the Persian Turandokht (daughter of Turan — referring to the Persian region of Central Asia). Turandot in Persian literature — appears in the iconic Persian-Italian collection Le mille e un giorno (1710-1712) by François Pétis de la Croix — the Persian medieval source. Princess Turandot — modern Persian-Italian heritage naming.
Turandot 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 Turandot reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.