Rapunzel is from the German Rapunzel — the name of the rampion plant (Campanula rapunculus), a small purple-flowered herb whose roots were eaten in salads in medieval Europe; in the Brothers Grimm tale, the girl is named for the plant her mother craved during pregnancy. The Brothers Grimm story "Rapunzel" was first published in their 1812 Children's and Household Tales — adapted by them from the 1698 French story "Persinette" by Charlotte-Rose de Caumont de La Force.
Rapunzel 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 Rapunzel reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.