Siân is the Welsh form of Jane — from the Hebrew Yohanan, meaning "God is gracious."
Siân Phillips (born 1933), the Welsh actress, is the most internationally known bearer.
Sian 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 Sian reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.