I do not completely understand the reason behind why we write our surnames before our given names when listing them on documents, usually separated by a comma.
EX: Donald Trump would sign "Trump, Donald"
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I suspect that the reason this is used in formal documents (note though, it isn't as ubiquitous as the question makes out - I have seen this being used on a ticket for instance one year, only for it to use the order of forename surname the next year) is to list the pieces of information in descending order of genericness (becomes more specific towards the right).
For instance - it's not hard and fast, but this is an example - people in your family share your surname, you are all members of your family, but to be specific you each have forenames which are presumably different. These forenames are an identifier for you within the context of your family. It is a little like labelling a person as one would an object, for example, "Apple Macbook Air" as opposed to "Air, Macbook, Apple" the former shows descending order of genericness as well, whereas the latter becomes more general towards the right like we would normally say someone's name.
I think the commas are probably to discern the order from the normal order, as with the Apple Macbook example, I felt I had to use commas to seperate the version in the opposite order, because this wouldn't make as much sense: "Air Macbook Apple". It would be perfectly valid - though strange - for someone to be called "Trump Donald", so by using the comma "Trump, Donald" you know that the expression refers to a "Trump", of type "Donald".
I'll expand on my comment a bit:
Alphabetization & uniqueness
Imagine a bouncer with a clipboard at the door of a nightclub. We all know what's on the clipboard: the guest list, which is an alphabetized list of names ordered by "Last Name" ascending. Why?
By maintaining a consistent order via alphabetization, optimization is better achieved. When checking in a guest, is the bounce quicker by rifling through pages of names in random order to find the guest, or is he better suited to index the list by a unique key to ensure fast lookup?
So since we know randomness if inefficient, if we're to maintain an ordered list of names, what might be the most unique property of a person's name? Well, the surname.
And by combining these two logical assumptions, we arrive at the behavior it manifests: ordered lists by last name.
This concept parallels to any other system that needs to catalog people. Physical documents will be filed away, again by last name, however when retrieving the document it's also much more natural for the eye to gravitate to the upper-left corner of the page, which by design, is the last name.