Hi,
Indeed, for some AJAX display, the system will skip the Joomla display mechanism to avoid issues.
There, you'll have to modify the view directly.
In the HikaShop configuration, under the Advanced tab, you'll find a setting "display view files" which you can activate in order to get displayed the name of the view / file on each area of HikaShop.
So it's a great way to find which view file is used where.
For the form you'll see when you add a new address on the checkout, it's the view file show_block_address that you can edit via the menu Display>Views.