Sarmistha is from the Sanskrit शर्मिष्ठा (Śarmiṣṭhā — most fortunate, most charming) — from Sanskrit śarma (joy/fortune). Sarmistha is one of the Sanskrit feminine names — central to traditional Hindu epic heritage. Sanskrit feminine name reflecting Hindu epic heritage.
Sarmistha 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 Sarmistha reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.