Siena is from the Italian city of Siena in Tuscany — also the burnt-sienna color (the deep reddish-brown derived from the natural earth pigments mined near the city). A top-500 US baby name since 2012. Siena Heights University — Michigan Catholic university.
and modern American naming.
Siena 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 Siena reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.