Look up origin of surnames: http://en.wikipedia.org/wiki/Family_name Pick a name, such as Miller. Miller is an occupational name. Say in Medieval Germany there were 1,000 mills (I have no idea how many; that is just a nice round number) scattered throughout Germany (of course, Germany did not come into existance until about 1858, but that is beside the point). The Mad King decreed everyone must choose a surname. So, across the country, 1,000 men chose Miller, as that is what they did.
Since German (or where Germany now exists) has experienced constant warfare ever since man first set foot there, the people of Germany come from hundreds of various tribes, some Germanic, but many, including Gauls & Huns, not Germanic.
So, at that time (about 1400 A.D.) there are 1,000 Miller families; probably only a few of them were even remotely related at that time.
Some moved to Poland, some to Russia, some to Austria or Switzerland, some to France, the Netherlands, the British Isles...and eventually some swam across the Big Pond to the American Colonies.
They probably weren't related in the first place (that is, not within the past 30+ generations or so), so how would they be related now?
With my own surname, which is an English surname, and before the Invasion by Mexicans one of the most common surnames in America, the British Isles and other places where Europeans migrated to, most of the people I meed by the same surname are blacks.
None of my ancestors (as far as I can track) ever held slaves; some even came to this country as indentured servants, which is a polite way of saying "slave".
The DNA testing companies as well as the genealgy sites claim that if you share a surname with someone that you have a higher chance of being related than if you do not share a common surname.
So, I will say, "It depends..." My grandparents were born in the 1860s; theirs from 1760 to 1790. Going back to Charlemagne and back to Imperial Rome, my families generations average about 35 years for women, 40 for men. So, for my standpoint, since the generations are longer, the chances of being related to someone with the same surname are greatly diminished. But, things are changing: the most common surnames in the U.S. now are Mexican....Giving me an even lesser chance of being related to people by the same surname.
My surname is one of those patronymic names, but the same analogy to Miller applies: people all over the B.I. suddenly started using the same surname.
So, it is not a case of having the same surname for "no reason", but because the same surname applied to so many families and after all, there is a limit to the number of words and hence names available.
More than 1/2 of the surnames at the time of the American Colonies are now extinct; at the same time, new ones are being coined to keep up with the rapid increase of human population.