@michael2015: "birth certificate with chinese name to your embassy or consulate along with his chosen English (or other foreign language) name"
To add to that, different countries also have different policies for managing the name itself.
For example in case of our son, if/when we were to apply for his foreign nationality and passport via my consulate, that would initially come with direct Pinyin transliteration of the Chinese first and middle names - we can not choose a better match at that point.
That would then be combined with my foreign last name.
If we (or he) want a better matching foreign name, we can then later separately file for name change to the name we want, same as any other citizen.
@German Shepherd: "foreigners doing business (e.g. bars, restaurants, etc.) [...] Do you maybe know what Visa category"
I don't really know what visa everyone is really on, but I can tell what they should be on (and what I am on).
If a foreigner registers a formal business in China, he/she can then also apply for Foreigners Work Permit to work in the foreign-invested company, and subsequently acquire Z-visa (I'm not sure if this is absolutely necessary if you would be already in the country) and work-related Residence Permit.
He can then work in the company doing any work that is in the scope of the business.
This is pretty much the usual process same as if the person worked in Chinese company, with one notable exception.
The person would be both the employee and the manager, and as such the person would handle both the employer and the employee parts of the application process.
That said, with all the relevant initial and annual administrative responsibilities and related costs, I would not personally suggest this option just to avoid "eternal boredom". Unless the hobby could bring a fortune too.
(if the foreigner were instead to invest millions, then the person would be eligible to Permanent Residency and that's a different story).
If it is a type of business where your visible presence would increase profits, then even if you don't take out salary and the PSB wouldn't mind otherwise, possible competing businesses may raise the issue with them.