Why was World War I was in its time refered to as the Great War, or
the War to End All Wars?

World War I was called "The Great War" mainly because it was the first
global war of that magnitude. All of the "great powers" were involved
in the war- making it unique in the history of warfare.

The "war to end all wars" phrase also refers to the magnitude of the
conflict and also was used as a justification for continued fighting-
that the war would be the one to end them all. It also refered to the
enourmous cost of modern warfare as many thought there would never be
another one again after witnessing so much violence.

http://en.wikipedia.org/wiki/World_War_I
"World War I has also been called "The Great War" (a title previously
used to refer to the Napoleonic Wars) or sometimes "the war to end all
wars" until World War II. The term "First World War", implying an
event distinct from a "Second World War" has fallen into disfavour by
some scholars who regard World War I as merely the first phase of a
three-decade long war spanning the period 1914?1945.4 "War of the
Nations" and "War in Europe" were commonly employed as descriptives in
the 1920s."

The War to End All Wars
http://en.wikipedia.org/wiki/War_to_end_all_wars
<<World War I (then known as The Great War) was at the time and in the
years just after described as the "war to end all wars" (or, in the
jargon of the French Poilus: "la der des der", i.e. "the last of the
last"). The phrase was in part a reaction to the horrors of the
conflict with many believing that with the full cost of modern war so
evident no nation would fight one again. It was partially an outgrowth
of the original reasons for going to war seeming insignificant as the
conflict dragged on, and the notion was adopted as an explanation for
why continued sacrifice was needed. The notion of the conflict being a
war to end all wars was also closely linked to the portrayal of
Germany among the Allies; the country was seen as the heir of Prussian
militarism, and a longtime warmonger. To end warfare, the defeat and
destruction of this militaristic power in the centre of Europe was a
necessity.

After the war a number of initiatives were taken to try to assert the
promise. This included the formation of the League of Nations, the
rewriting of the map of Europe, the Kellogg-Briand Pact outlawing war,
and a number of other treaties limiting military power.

With the outbreak of World War II the phrase quickly began to be seen
ironically; in an episode of M*A*S*H, Colonel Potter remembers his
fallen friends, one who died in "the war to end all wars," and one who
died in "the war after that.">>

Google Search Strategy
"the great war"
"war to end all wars"

Some very good information posted by adiloren-ga.

However, I noted your question asked why WWI was know by various names
DURING WWI, not afterwords. That is, if I understand your question,
you are asking why did people living in the years 1914-1919 call their
war The Great War, or The War to End All Wars?

Again, adiloren touched on it. But it boils down to convenience of
terms, what we in the early 21st century refer to as "sound bytes."
It's simply a shorthand way to reflect what was happening in France,
the Baltics, Germany and other places. No special reason, in other
words. It could have been called the Trench War, easily enough, and in
fact that term was used but does not survive to this day.

Primarily it was a news and press convention. Civilians and
politicians picked up the new terms and ran with them. Much the same
as The Gulf War in 1990-1991. No one "officially" tagged that war by
that name. It just came to be, mostly through its common use in the
press. Still, unless one actually knew about that war (say, anyone
under 12), an American might think "Gulf War" was a reference to the
Gulf of Mexico, perhaps, and leave them wondering just why we had a
war with Mexico in 1990. You might just as easily ask why people alive
in 1990-1991 referred to it as The Gulf War, and fifty years on when
it's name may certainly have changed, why did it change?

You might think of the naming process the same as we call our
sensational trials: The OJ Simpson Trial, The Enron Trial. Nobody
officially gave them those names, yet they are what we read in the
press and how civilians speak about the trials.

Once a common term for a war seems to be in wide use, it merely
becomes convention, de facto, and everyone uses it from that point.
But to be fair, until that particular war came to be, there had never
been a theatre so vast that involved so many nations all at the same
time. It truly was "Great" (meaning, BIG, not wonderful). That had a
lot to do with selecting the term "Great."

The description ?great war? was a recognition that this was a war
which was to involve several countries and was potentially
devastating.
 
Throughout the 19th century the Times newspaper refers to the
Napoleonic wars as ?the great war?. Note the lower case.  Many other
publications used the same phrase including a fictional account of
?The Great War of 189-?.
http://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/pityofwar.htm

Shortly before the outbreak of war the Times editorial commented that,
?Europe is on the verge of a war more general and more terrible even
that the ?Great War? of a hundred years ago.?
Jul 30, 1914 

Upon the outbreak of war in August 1914 there was a great demand by
the public for information, and the Times, always ready to make money,
published maps and a serial magazine titled ?The Great War. The
Standard History of the All-Europe Conflict? edited by H.W. Wilson. It
was described as the ?standard history of the stirring events which
are now taking place.? Despite the popular feeling that the war would
be over by Christmas, it was clearly thought that this was a
worthwhile publishing venture.

As you know, the war did not finish by Christmas 1914, and the
magazine went on to end up in 13 large-sized bound volumes. You can
see more information here.
http://www.greatwardifferent.com/Great_War/NewsMedia/GreatWar.htm

At the same time Madam Tussauds mounted an exhibition called ?The
Great War: defenders of our Empire?, with models of various generals
and admirals.

From the on in the Times, it is described as the great war, or the
Great War. Of course, the Times is only one source. You would have to
research other sources to see if this was a generally held view.

You may not be aware of this recruitment poster of the time: Daddy,
What did YOU do in the Great War?
http://www.firstworldwar.com/posters/images/pp_uk_07.jpg


The first Times reference to ?War to End All Wars? is in 1920. A
letter to the Times describes it as a ?catchphrase?.
?War to end wars? is 1931.

Hope this has been of additional help.
answerfinder-ga