Carly is a 20th-century American feminine of Carl — Old Germanic karl (free man). Carly Simon (born 1943) — *American singer-songwriter; 1972's You're So Vain — about an unnamed lover whose identity she partially revealed only in 2015 (Warren Beatty for the second verse) — spent three weeks at #1. Two Grammy Awards; Songwriters Hall of Fame (1994). "Nobody Does It Better" (1977 The Spy Who Loved Me theme), "You're the One," "Coming Around Again," "Let the River Run" (Oscar 1989). Carly Rae Jepsen (born 1985) — Canadian singer; Call Me Maybe* (2012) topped charts in 19 countries and is among the best-selling singles of all time. Carly Fiorina (born 1954) — former Hewlett-Packard CEO and 2016 presidential candidate.
Subject of Carly Simon's memoir Boys in the Trees (2015).
In Pythagorean numerology the letters of Carly reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.