It sounds like you are unclear about the origins of your name though? If the name doesn’t have Japanese origins it is usually seen as odd to write it in Kanji
Are you Japanese? If not it’s just English. There wouldn’t be a specific kanji for it since there are a lot of characters with that pronunciation
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There are many possible kanji for that name
https://jotoba.de/search/%E3%81%8B%E3%81%84?t=3&p=1&l=en-US
if you don’t know what it is, there’s no way we can guess.
I mean, the name “Kai” has origins that can be found in many languages, but sure there Japanese names written in Kanji that sound like “Kai”
https://jisho.org/search/kai%20%23names
It sounds like you are unclear about the origins of your name though? If the name doesn’t have Japanese origins it is usually seen as odd to write it in Kanji
Are you Japanese? If not it’s just English. There wouldn’t be a specific kanji for it since there are a lot of characters with that pronunciation