Generally, countries' systems only handle characters in names that are common in that country. Virtually no banking or ID system in Europe or the USA will handle Chinese names, for example. Even if they did at the technical level, it wouldn't actually help at a holistic level, because people who interact with these systems (bank tellers, policemen, etc) can't be expected to recognize any writing system in the world.
So, the reality is that you have to adapt to the country you're trying to live or do business in and the name systems that they can actually use. This can even mean you have to adopt a name that people can actually pronounce, as many Chinese people do when interacting with people outside East Asia
For example, Chinese is particularly sensitive to tone accent, which extremely few people outside that area can even distinguish, leading to hopeless mispronunciation. Consider that Ma2 and Ma4 are completely different words for a Chinese speaker, while a French speaker who hasn't studied this wouldn't even be able to tell that you are intentionally pronouncing things differently and not just your intonation.
And for a reverse example, if you want to move or do business in Japan, you should adopt a well-known Japanese pronunciation of your name, as otherwise Japanese speakers, who have an extremely limited syllable inventory compared to most other languages in the world, will just not be able to follow your name.