Maitreyi (मैत्रेयी) is from the Sanskrit maitrī (friendliness, loving-kindness). Maitreyi (c. 8th c. BCE) was the Vedic philosopher and wife of the sage Yajnavalkya — when he proposed to renounce the world and divide his wealth between her and his other wife, she famously asked: "Will this make me immortal?" — initiating one of the greatest philosophical dialogues in the Upanishads.
Featured in the Brihadaranyaka Upanishad.
Maitreyi 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 Maitreyi reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.