Branca is the Portuguese form of Blanche — "white." Branca of Castile (1259-1321) was the Castilian princess and Queen of Portugal through her marriage to Afonso III. Multiple medieval Iberian queens bore the name.
Used widely in modern Portugal.
Branca 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 Branca reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.