One surname for the whole world
This is not a dream, but something that may actually happen.
This theory says that in the end we will all have the same surname.
The assumption is based on the simple fact that surnames can die out, disappear and do not come back. This means that as long as new ones are NOT created there will be less and less surnames. Eventually this means that in the year "indefinite" only one surname will be left over for the whole world.
As the word "indefinite" suggests, this will of course take a very, very long time. And the last step from two surnames to one surname would probably take the longest. One could imagine that at a certain moment 95% of the world is called Zhang and the remaining 5% Smith and that the Smith's simply do not get married to Zhangs for reasons of protecting their own heritage. (sorry for oversimplifying this and neglecting some other candidate surnames such as Singh, Lee, Kim and Schmidt).
A more essential problem is that there are still countries, where the surname is after the first name of the father. I actually know of only one such country and that is Iceland. So when a Icelandic father with the first name "Tractor" gets children, the new surname "Tractorson" is created. (But in order not to have the new surname die out after one generation this kid would have to emigrate out of Iceland.)
Assuming that Iceland will at some time disappear in the sea or is forced to abolish its medieval name system under pressure of an expanded European Union, we will eventually all have the surname, unless
So unfortunately we are not going to see this theory proven in the end, but we can still see the effects at this moment.
In China one can see what it means for a country to have the same surname system for a couple of thousand years, there are only a couple of hundred surnames for a country of 1.2 Billion people. The Netherlands, however, still have a very rich variety of surnames, as the current surname system is less than 200 years old. In that relatively short period I guess that more than half of the surnames have disappeared in the Netherlands.