Saranyu (सरण्यू) is from the Sanskrit root sṛ ("to flow, run"). Her cosmic chase by the sun is one of the myths of the Rigveda.
Featured in Rigveda 10.17.
Saranyu 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 Saranyu reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.