Do I need an affidavit for name change for spelling of my child’s middle name?

I recently gave birth to my son and am preparing to report his birth to the consulate in Osaka.

We gave him the middle name ‘Jonah’ on his Japanese documents in katakana ジョナ. Since this would technically be romanized ‘Jona’ so I’m wondering if I need to prepare the affidavit/statement of name change since technically the spelling I want on his American documents reflects differently from his Japanese documents?

This may seem like a silly question, but when we applied for his Japanese passport the staff there were all in a tizzy that we wanted to add that final letter ‘h’ to the katakana romanization of his name so now I’m second guessing the American documents too 😅