Willow is the English word for the tree (Salix), known for its long flexible branches and association with watersides.
Willow's use as a girl's name is recent. It rose into the U.S. Will Smith and Jada Pinkett-Smith's daughter Willow Smith is a singer who has kept the name highly visible.
Willow 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 Willow reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.