Shruti is from the Sanskrit śruti (श्रुति — that which is heard, sacred hearing, divine revelation). 800-200 BCE); the iconic Sanskrit Shruti (revealed knowledge) is contrasted with Smriti (remembered knowledge); central to traditional Hindu religious philosophy. Princess Shruti — Hindu heritage naming.
Shruti 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 Shruti reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.