Savita (सविता) is from the Sanskrit savitṛ — "the one who brings forth, the sun" — one of the names of the Vedic solar deity Savitr, who is invoked in the most sacred of all Hindu prayers, the Gayatri Mantra (Rigveda 3.62.10), recited daily by millions of Hindus for over 3,000 years. B.R. Savita Devi — Indian classical thumri singer. Savitri is a closely related Sanskrit name (covered separately) — the devoted wife who won her husband back from Yama, god of death.
Savita 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 Savita reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.