Gita is from the Sanskrit गीता (Gītā — song, sacred song) — from Sanskrit gai (to sing). Gita is one of the Sanskrit feminine names — central to traditional Hindu Vedic heritage. Sanskrit feminine name reflecting Hindu philosophical heritage.
Gita 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 Gita reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.