Asmar is from the Assyrian / Arabic أَسْمَر (Asmar — dark-skinned, brown, dusky). Asmar is one of the Assyrian + Arabic feminine names — central to traditional Levantine + Mesopotamian heritage.
Asmar 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 Asmar reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.