Fina is the Italian short form of Serafina ("burning one"). Saint Fina (1238-1253) was the bedridden Italian mystic of San Gimignano who, when she died at fifteen, made white violets bloom on her wooden plank-bed. The violets of San Gimignano are still called "Saint Fina's flowers."
Featured in Ghirlandaio's frescoes in the Collegiate Church.
Fina 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 Fina reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.