Vital statistics and civil rights, including the name(s) used in the exercise thereof, in general are regulated by each province.
No province keeps a register of residents like many other countries do and no person is required to register with the government for simply living in Canada. Neither the federal government nor the provinces have a database of Canadian citizens. There is no "authority" who determines one single legal name for every person legally present in Canada. There is not even a requirement that a province needs to recognize one's change of legal name legally made in another province (e.g. Quebec often does not recognize officially the change of name made by a Quebec-born person outside Quebec since its civil code imposes stricter requirement on the change of name, compared to other common law provinces).
Instead, in practice, the legal name in Canada, for an administrative or legal purpose, is the name written on whatever documents deemed acceptable by an authority for that purpose. Other than a Canadian birth certificate, an immigration, citizenship or passport document issued by the federal government is often the most accepted type of documents to establish identity and legal status in Canada. So it is not necessarily wrong to say that this constitute an "implicit" change of name, but it is hard to find documentation to prove it.
Now many provinces do have a general rule or law for Canadian born persons that the legal name should be the one recorded on their birth certificate (even if in practice, it is not so simple, e.g. with marriages or change of name declarations made in another province or a foreign country). For example, in Alberta:
(l.1) “legal name” means
- (i) in the case of a person born in Canada, the person’s name as shown on the birth record of that person, or
- (ii) in the case of a person born outside Canada, the person’s name as shown on the documents satisfactory to the Registrar;
But as you can see, for a person born outside Canada, the legal name is the name shown on a "satisfactory" document, which may include all sorts of government documentations, domestic and foreign, that may reflect different names.
A tangential clause in the Alberta law may be useful to you:
22(1) In this Part, “name”, in addition to the meaning assigned to it in section 8, means [...] (b) in the case of a person born outside Canada, the person’s name as shown on the documents under which the person was lawfully admitted to Canada.
However, (1) this is not a definition of "legal name" which is defined as any name that is on an acceptable document, but "name"; (2) the definition only applies within the context of a change of name application in Alberta ("In this Part"); (3) the document under which a Canadian citizen was lawfully admitted to Canada is not necessarily their Canadian citizenship certificate or passport (a permanent resident, admitted under their foreign passport and PR card, may become a citizen without leaving Canada). But if all you need really is some sort of official sounding thing that may satisfy some bureaucrats abroad, this may suffice.
One practical problem is that when visiting the birth country the name they know him by isn't an exact match of what's on the passport, citizenship card, and other ID, and that confuses the clerks and officials. A formal change of name document would help, but there isn't one. It would help a lot to be able to point to an official Canadian law that explicitly says that the Citizenship name is an implicit legal change of name.
It is often a messy issue. If it really becomes a significant issue, you may be able to resolve it by making some sort of legal declaration under local law (e.g. before a notary public or consular official), or try to request an observation on your passport.
You can of course, also request a declaration of legal "change" of name in your place of residence according to the relevant provincial law.
Similar situations also happen to e.g. naturalized former Chinese citizens who "lose" their legal name in Chinese characters. They are often required to prove that they are themself if they want to e.g. sell their assets held under their Chinese name. The usual course of action is to declare under penalty before a notary public, or to have a certified "same-person declaration" done before a consular official.
It also happens to some Chinese persons born abroad, who have a non-Chinese name (or otherwise not conforming to Chinese naming requirements) inscribed on a foreign birth certificate, but cannot use that name on their Chinese travel document or civil register. In that case, consular officials may inscribe an observation on the passport noting that the holder is also known under another name.
Update (from the OP):
You can of course, also request a declaration of legal "change" of name in your place of residence according to the relevant provincial law.
I've now found someone in a similar situation (dropping the Chinese given names) that did exactly that (in 2008).
Their application was returned for reason "Other":
Written on it was:
According to our office, your current legal name is "[redacted]" (the name that appears on the back of your Canadian Citizenship Card). Therefore, a name change is not required.
So apparently whatever appears on one's Citizenship Card is their legal name (at least as far as Ontario is concerned).