From the experts:
Common in Wales, this name was introduced to America when Welsh-born Catherine Zeta-Jones and husband Michael Douglas chose it for their daughter in 2003. It didn't come into use in Wales until the late nineteenth century. It's currently Number 367 in England and Wales.
Carys is one of that sweet group of girls' names with a loving meaning, and this has a subliminal link to the word 'caress.'
Cerys is also heard in Wales.