From January 2020, Japanese names in national documents will be written in Roman letters in principle in the order of "Last name → First name" and all surnames will be capitalized. What used to be "Shinobu Unakami" is now "UNAKAMI Shinobu". There is no enforcement force, but I think many iPhone users will change their email sender name to "Last name → First name".
However, the procedure for changing the email sender name on iPhone is slightly different between iCloud Mail and other accounts. It's complicated, so let's organize it.
For accounts other than iCloud Mail, go to "Settings" → "Password and Account" screen. In the case of the mail account (POP) given by the contracted provider, tap the account name and edit the name field on the screen that appears.
Gmail does the same, but taps more than most providers. Tap the account line (Gmail email address) on the screen that appears when you tap the account name. This will bring up a screen where you can edit the name.
ICloud Mail is hard to understand. When you tap the iCloud account line on the "Password & Account" screen, you will be taken to the Apple ID setting screen (the same as "Settings"> "Apple ID"), so tap the "iCloud" line.
Then, the screen will change to the screen showing the consumption status of iCloud storage, so let's scroll to the bottom of the screen. The "Mail" line there is the entrance to the screen where you edit the sender name for iCloud mail. It's hard to notice if you have a lot of apps installed, so please repeat the flick.
Easy operation procedure explained