Carys is the Welsh name from caru (to love) — meaning "love" or "loved one." A modern Welsh creation that became widely used.
Carys Zeta Douglas (born 2003) is the daughter of Catherine Zeta-Jones and Michael Douglas.
Carys 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 Carys reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.