I admit I don’t know. I suspect they may be required to select one or two as legal surnames in the Quebec system and the rest become middle names. I’m not aware of a limitation on quantity of middle names.
I actually gave my son my surname as a middle name because I didn’t want to double barrel. He’s got 4 names total. A friend of mine has 7, only one is his legal last name.
Saudi Arabia is good for having four names; how do you put that into three fields for First, Middle, & Last, which is the standard ‘American’ coding.
Ah, yes. The Mark of the Beast. (I am being sarcastic of course).
I have the opposite problem. I just have two names, a first name and a last name/family name. Sometimes that causes problems with American forms that demand a middle name, or at least a middle initial.
That’s a simple fix, put in N…for None. 
Sure, but there is (thankfully) no unified numbering scheme for individuals. Many countries have something similar at national level, such as the social security number in the US, but as soon as people from different countries come into play, this won’t work. So the traditional system of personal names is the best think we have to identify individuals unambiguously - perhaps augmented with other personal data, such as birthdates.
The Navy (as well as, presumably, the other armed forces) uses NMI – No Middle Initial.
My son has two middle names (but only one last name). My wife and I come from cultures with very different middle naming schemes, so we gave him one from each scheme.
Don’t forget Johann Gambolputty <…> of Ulm.
You may write the name out, everything else lacks respect:
Johann de von Ausfern-Schplenden-Schlitter-Crasscrenbon-Fried-Digger-Dingle-Dangle-Dongle-Dungle-Burstein-von-Knacker-Thrasher-Apple-Banger-Horowitz-Ticolensic-Grander-Knotty-Spelltinkle-Grandlich-Grumblemeyer-Spelterwasser-Kurstlich-Himbleeisen-Bahnwagen-Gutenabend-Bitte-Ein-Nürnburger-Bratwustle-Gerspurten-Mitzweimache-Luber-Hundsfut-Gumberaber-Shönendanker-Kalbsfleisch-Mittler-Aucher von Hautkopft of Ulm
IT guy, here. We’ve got 10 characters available to identify someone in our system. And they can’t ever repeat a previous entry. It gets painful sometimes.
Ten characters would not be enough for my name, but if that makes me non identifiable then it might not always be to my disadvantage. Or so I like to believe. The fact that the Spanish part of my name tends to confuse German administrators and the German part of my name does the same to the Spanish administrators has not harmed me either, so far, probably, I hope.
I am now imagining an unpublished Borges story about a person whose name was so long it could not be completely spoken before the heat-death of the universe…
I am imagining an unpublished Borges story about a writer who wanted to write that story but failed because he considered it indispensable to include the name in it.
The name is probably somewhere in the Library of Babel.
Then again, maybe not: that only contained only 410 page books, apparently.
There are infinitely many more…
Not so. I am not giving out my SSN (or Canadian SIN) to anyone unless they have a need to know (an employer or a bank).
As stated above, Quebec limits you to two family names. And you are stuck with your birth name for any government use.
This makes a lot of sense, I have this teacher who’s last name is 18 letters long but she shortens it to the last 6 letters of her name.
There has been at least one person at my work with one name. Not “family name”, not “personal name”, just “name”.
I’m pretty sure the passport forms have special instructions for this eventuality.
Then there’re people like me, who insist on the middle name being present. In my case it was because of a horrible incident at school, where I was accused of something* I could not physically have done. At the office, they realized that someone with a different middle name had done it…
* Parking violation. I did not own a car and couldn’t drive…
I have a friend in this situation. He has been using his father’s single name as a surname just to satisfy the bureaucracy here, but in his country of origin it’s just the one name.
Let me guess: Indonesian?