IIRC, one have to edit some joystick description file, which is loaded by JoystickTweaker to enhance and set more user-friendly and defined names to device features.
EDIT: giving a look to JoystickTwearker source, it show that indeed the device name (which GetControllerName() returns) and others descriptions are loaded, when found, from a joystick description file that should be located in /boot/home/config/settings/joysticks/ (for an USB joysticks, that would be .../joysticks/usb/0 etc), with a syntax like this:
(only usefull for old gameport-based joystick, usb sticks are dynamically detected by usb_hid kernel module
(that's your ControllerName string, by default a "2-axis" should be returned according API spec, but it's not the case)
and those below, to statically declare stick features for gameport-based joysticks.
It's useless for USB sticks are there info are dynamically retrieved from USB HID report
So, @dragon, try to create a /boot/home/config/settings/joysticks/usb/0 file with this content:
module = usb_hid
gadget = Here your gamepad controller name
(Beware, code expect gadget=, so space around the equal are mandatory)
and check if it change something.