Girija is from the Sanskrit giri (गिरि — mountain) + ja (ज — born) — "mountain-born" — the iconic epithet of Hindu goddess Parvati (born of the Himalayas). Princess Girija — Hindu heritage naming.
and Hindustani classical music.
Girija 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 Girija reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.