Carol is a feminine of Charles (from the Old Germanic karl, "free man") — also from the Middle English carole (joyful song, dance). A top-10 US baby name from 1939 to 1953, peaking at #4 in 1942. Carol Burnett (born 1933) — the *American comedian whose The Carol Burnett Show (1967-1978) won 25 Emmy Awards and pioneered the female-led variety show. Carol Channing (1921-2019) — Tony-winning Broadway actress and originator of Hello, Dolly!. Patricia Highsmith's Carol (originally The Price of Salt, 1952) — among the first widely published lesbian novels with a happy ending.*
Subject of Todd Haynes's Carol (2015 film).
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.