What theories do linguists have for explaining the difference across
languages/cultures in the length, number of syllables, and complexity
of words of different languages, specifically family names?  Might
this have anything to do with climate?  E.g. Southern Indian
Sub-continent, and African sub-Saharan names, tend to be long with 3-6
syllables, while those from further North, from cooler, dryer climes
tend to be short.

THERE IS ONLY ONE ANSWER; Like it or not, from the Bible, Genesis 11;
5-9 "5 And Jehovah proceeded to go down to see the city and the tower
that the sons of men had built. 6 After that Jehovah said: ?Look! They
are one people and there is one language for them all, and this is
what they start to do. Why, now there is nothing that they may have in
mind to do that will be unattainable for them. 7 Come now! Let us go
down and there confuse their language that they may not listen to one
another?s language.? 8 Accordingly Jehovah scattered them from there
over all the surface of the earth, and they gradually left off
building the city. 9 That is why its name was called BaŽbel, because
there Jehovah had confused the language of all the earth, and Jehovah
had scattered them from there over all the surface of the earth.

I'm sure wschloss-ga was looking for an answer not based on mythology.

Check out this site and the links to other on Wikipedia.

http://en.wikipedia.org/wiki/Origin_of_language

In defense of Pugwash, the site includes a picture of the tower of
Babel and starts with the Bible story.

In the 19th century, there were some suggestions that cultural were
tied to climate.  Not surprisingly, the theorists found that their own
climates were conducive to the development of superior traits.

These arguments have no significant following today because there are
so many counter-examples.  You'll find plenty of long names in
Iceland, Finland, or Poland--and in Iran, Madagascar, or Thailand.  In
short, when you start collecting evidence, any apparent correlation
between syllable counts and climate doesn't hold up well.  Another
problem with "climate theories" is that ethnic/linguistic groups have
been moving around--and not just in the Industrial Age.

You might be interested in reading about the Sapir-Whorf Hypothesis,
http://en.wikipedia.org/wiki/Sapir-Whorf_Hypothesis  or do a Google
search.

It doesn't directly answer your question, and the hypothesis is
largely discredited, but you might find it interesting.

And it isn't true, as another comment said, that people from northern
climates have shorter names always, or that languages in northern
climes have shorter words.   Both Iceland and Finland, off the top of
my head, are examples.  Finnish has some of the most complex words and
morphemes in the world, and Icelandic surnames are quite long (not
sure about the language itself). I'm sure you know those are two of
the coldest countries in the world.