Sea, ocean, or open water
Kaien is a modern name often used as a variant of the Hawaiian name Kai, meaning sea. In Japanese contexts, it can be formed from kanji meaning 'ocean' and 'salt' or 'boundary,' though its usage in the US is primarily as a creative phonetic variation.
Less common today
Kaien isn't in the latest US Top 1000. It last peaked at #6,298 in 2016.
US births per 5-year period, 1990βpresent (SSA data).