Juliet is the English form of the French Juliette — a diminutive of Julie, ultimately from the Latin Julia, the feminine of the Roman family name Julius.
Shakespeare's Romeo and Juliet (c. 1595) made the name eternal. Today Juliet sits in the U.S.
Juliet 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 Juliet reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.