Cora comes from the Greek Korē (Κόρη), meaning "maiden" or "daughter" — and a title used in Greek myth for Persephone, the daughter of Demeter, in her aspect as the queen of spring before her abduction by Hades. Persephone is sometimes simply called Kore, "the Maiden."
Cora's modern use in English comes from James Fenimore Cooper's 1826 novel The Last of the Mohicans, where Cora Munro is one of the heroines. The name climbed steadily through the late nineteenth century, faded, and has returned with surprising vigour in the 2010s.
Cora 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 Cora reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.