Long live the Queen and her successors
It's a matter of choosing which name will be your primary name, which is closely related to how the person identifies. If they identify, for example, as a native of Northern Ireland born from parents from Hong Kong then they're more likely to use their Western name than their Cantonese name, and if they identify more towards their Hong Kong identity they're more likely to use their Cantonese name. And with Oliver Zhang, when he's not in Japan he always uses Oliver Zhang and has never used Zhang Ruizhong (at least, as far as I know). So in this case it's more likely that Oliver Zhang is his 'original' name.That's an interesting debate in itself.
I have a number of friends whose families were originally from Hong Kong. (So, they speak Cantonese rather than Mandarin). They were all born in Northern Ireland. One set of siblings primarily use their Anglicised names in everyday life. The other set of siblings primarily use their Chinese names in everyday life. The interesting thing is that the 2 sets of siblings are cousins.
So, it is not straightforward.
Going a bit off-topic, but I do hate the notion that a lot of Western people have that second-generation folks in the Western hemisphere are supposed to have their parents' culture name as their 'original' name. Like, for instance, the snowboarder Chloe Kim has a Korean name (Kim Seon) but she never goes by it, her name for all intents and purposes is Chloe Kim. Even in Korea people call her Chloe Kim and not Kim Seon. Yet some people assume that Kim Seon must be her 'real'/'original' name, it drives me nuts.