Gayatri is from the Sanskrit gāyatrī (the sacred Vedic verse). The Gayatri Mantra — the Hindu sacred chant; addressed to the sun deity Savitr; appears in the Rigveda (Mandala 3.62.10) — the oldest extant text in any Indo-European language (composed c. Gayatri Joshi — Indian Bollywood actress.
Gayatri 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 Gayatri reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.