Hepburn or Non-Hepburn Transliteration for Use Outside Japan

I previously posted about handling name change after naturalizing. Now, I have another question regarding name change, and I would greatly appreciate any advice.

Let’s say, before naturalization, my name was Biden Joe, and after naturalizing, I changed it to Trump Joe. I registered トランプ ジョー (Toranpu Joo) in the Japanese records, such as 戸籍 (koseki), my bank accounts, etc.

Now, when it comes to passport, I know the name will be written as Toranpu Joo in Hepburn style transliteration. However, I believe there is an option to add the non-Japanese reading of the name if it’s of foreign origin. So, my passport could potentially show something like Toranpu (Trump) Joo (Joe).

My question is about how this impacts my name on credit cards and when booking international flights:

• Can I choose to have Trump Joe on my credit cards, so that when I travel abroad, I can use the English spelling for tickets, hotel bookings, etc.?
• Or, will I need to use Toranpu Joo on credit cards and bookings to match my official Japanese records?

Thank you in advance.