I am not a hacker nor security expert, so take this with a grain of salt. As I see it, there's one of two (general) ways a group will get a name:
1) The group themselves declares it (like Anonymous). Which means they need to explicitly leave their name somewhere.
2) The name is given by someone from the outside, such as the US.
I suspect 2 is quite common. I wouldn't expect most state level hackers leaving calling cards on systems. In fact, probably not most hackers at any level. It really seems like if state level actors were leaving calling cards that this would instead be misdirection rather than a tag. So I would not be surprised if they ended up getting US style naming schemes because it would be US (or other Westerners) identifying these people the same way you'd identify people by the style of actions and how they write. I know you can probably look at code from coworkers and know who wrote specific parts. Think like what you see in a movie with serial killers (or even real life). How do you know it is the same killer? Style.
I mean you could also get the name if you infiltrated the other country and then intimately studied their groups. The name of their group internally. But then you'd probably translate it. Still probably not a great idea to give that name out publicly though because then you could be hinting at how you obtained that information because different parts of the organization may refer to the same group by different names (specifically to do this. Military groups often run disinformation internally in secret channels).
Edit: guessmyname left a link to showing Microsoft names these.
https://www.microsoft.com/en-us/security/blog/2023/04/18/mic...
https://news.ycombinator.com/item?id=39372339