Azar (آذر) is the Persian word for "fire" — also the 9th month of the Iranian calendar (November-December). In Zoroastrianism, fire is sacred.
Azar Nafisi (born 1948) is the Iranian-American author of Reading Lolita in Tehran.
Azar 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 Azar reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.