Total # of Family Names Approaching One?

Factual Questions
1

Isn’t the total number of family names in the world
slowly approaching one?

Here in America, when a woman marries, she usually
(but not always) takes the last name of her husband.
Any children will have this same last name.

Now, I realize that not every culture has the same method
for continuing family names, but surely no matter
what a culture does, some family names will simply
die out through lack of heirs. I think I already
heard that something like this is happening in one or
both of the Koreas where a large proportion of the population has the family name Kim, Lee or Park.
And I don’t know of any culture where family names
are being made up of whole cloth anymore. I know
that family names are a relatively modern convention
in many cultures.

Side questions: If, in some distant future, the
entire population finally all had the same family
name, what would that name be? And when might this
happen?

markle9

2

A previous take on the subject: Last Names

3

I have put this question through the great Mathemacomputer.
And the answer is this:
Smith, in the year 2654.

4

Actually, new names are still showing up continually. In a friend’s family, for instance, neither of the parents wanted to give up their own name when they married, so they both took a new name that was a combination of the two.

Even if we assume that no new names are appearing, though, it’s a lot slower process than you’d think, especially once you get down to two or three dominant names. Suppose you’ve got noboty left but Smiths and Grazowskis. Sometimes, you’ll have a marriage where a Smith turns into a Grazowski, and sometimes, (about as often), you’ll have a Grazowski turning into a Smith, so it (almost) balances out. The proportion of the population with any given name changes by a “random walk” process, which won’t get you very far, very fast.