Azeb is from the Ge'ez/Amharic አዜብ (Azeb) — south, south wind. Azeb Mesfin (born 1958) is an Ethiopian politician and businesswoman — wife of former Ethiopian Prime Minister Meles Zenawi (1955-2012) and First Lady of Ethiopia (1995-2012).
Azeb 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 Azeb reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.