Amutha is nectar, the sweet drink of immortality — and by extension anything utterly sweet and dear. It is love expressed as flavour.
Amutha 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 Amutha reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.