Geeta is from the Sanskrit gītā (song) — also the Bhagavad Gītā. Geeta Dutt (1930-1972) was an Indian Bengali playback singer — one of the voices of Indian cinema's golden age (1940s-1960s) alongside Lata Mangeshkar and Asha Bhosle. collaborations with composer S. D. Burman. Married filmmaker Guru Dutt (1953-1964, until his death).
Geeta 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.
In Pythagorean numerology the letters of Geeta reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.