Caelyn is a modern American compound name combining the Irish Caol (slender, slim) with the -lyn ending. A top-1000 US baby name since 2013. Caelyn O'Brien — American gymnast.
Caelyn 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 Caelyn reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.