Azalea is from the Greek azaleos (dry) — the botanical name for the genus of flowering shrubs in the rhododendron family, famous for their spring blooms in pink, white, red, and purple. Native to Asia, Europe, and North America; cultivated in Western gardens since the 17th century; the Indica azalea (introduced 1808) is the floral emblem of São Paulo, Brazil. A top-1000 US baby name since 2012. The Augusta Masters Tournament's 13th hole is named "Azalea" — among the most-photographed holes in golf because of the 1,600+ azalea plants surrounding it. Azalea Banks is Azealia Banks (different spelling).
Azalea 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 Azalea reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.