Caoimhseach is from the Irish Caoimhseach — variant of Caoimhe from Irish caomh (gentle/precious/dear). Caoimhseach is one of the Irish feminine names — central to traditional Irish heritage. Irish feminine name reflecting Celtic Christian heritage.
Caoimhseach 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 Caoimhseach reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.