Should I register my name in Katakana or Kanji for my Resident Record?

Hi all,

I am moving to Japan in March, and I was wondering what you think is the most appropriate way to register my name?

For context, I am known as Kai and wish to register this name for my Resident Record.

My last name will be in Katakana. Should I register my first name as Katakana as well, or is it acceptable for me to adopt the Kanji, 海 ?

For context, I am a woman of Chinese descent but never officially registered my Chinese name anywhere (except for work where it’s spelled out in English alphabet).