Carly is a 20th-century American feminine of Carl — Old Germanic karl (free man). Two Grammy Awards; Songwriters Hall of Fame (1994). 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 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 Carly reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.