Pure
Caitlain is a rare phonetic spelling variant of the Irish name Caitlin, which itself is the Irish form of Catherine. The name ultimately derives from the Greek name Aikaterine, which has been associated with the Greek word katharos, meaning pure.
Less common today
Caitlain isn't in the latest US Top 1000. It last peaked at #8,425 in 1990.
US births per 5-year period, 1990βpresent (SSA data).