Karen is the Danish form of Katherine — from the Greek katharos (pure). A top-10 US baby name from 1957 to 1968, peaking at #3 in 1965. Karen Blixen (1885-1962) — pen name Isak Dinesen — Danish author of Out of Africa (1937) and Babette's Feast (1958). Karen Carpenter (1950-1983) — American singer and drummer of The Carpenters; her death from anorexia nervosa at age 32 transformed American medical and cultural awareness of eating disorders. Karen Uhlenbeck (born 1942) — American mathematician; first woman to win the Abel Prize (2019).
Subject of the 2007 film Becoming Jane and Sydney Pollack's Out of Africa (1985).
In Pythagorean numerology the letters of Karen reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.