Carol is a feminine of Charles (from the Old Germanic karl, "free man") — also from the Middle English carole (joyful song, dance).
Subject of Todd Haynes's Carol (2015 film).
Carol 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 Carol reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.