What a nightmare.... maybe they should just start giving themselves a second name? We are not living the Napoleon ages anymore. Seems like common sense thing to do...
It would be more efficient to just adopt 16-digit unique identifying numbers. I suspect that wouldn't be popular.
In some countries, people take new last names because their family name is too common (eg Denmark and Christiansen). It's up to them.
It works in different places because of cultural norms and what they want/need from their naming systems. Some are perfectly fine and identify an individual from both father and grandfather, some use both parents' family names, etc.
Some in Canada do end up adopting last names, but it won't be imposed on them. A fair number of the issues that come up here in this regard are - as in this thread - because of mismatches between the different systems, or inconsistent use of them in some countries (eg more than one name being used in given name or family name space, and none in the other).
It's still up to the individual, you can pretty much change your name at will in Canada.