A question that has been asked probably a million times in this forum...

But when were WWI and WWII given those titles?

As a collector of all things old and dated, I have amongst my souvenirs, a large collection of old-time radio shows dating to as far back as the 1930s. In some of these shows, (in the early 40s, during the War), some of the people clearly start labelling the "Great War" as WWI. Did people start doing this the moment WWII started? Or was it a gradual thing that people began to realise that this was "the next big thing"?

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Parker '51' fountain pen.

It was gradual. Today some people still call WWI the Great War and depending on the nation WW2 has other names. But in English WW1 and WW2 are common and gained their names during and after WW2.

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The Muslim Brotherhood “must understand that their work in America is a kind of grand Jihad in eliminating and destroying the Western civilization from within and ‘sabotaging’ its miserable house by their hands..." — Mohamed Akram. http://jihadwatch.org/

and an answer, at least from the USA's point of view:

"Retiring War Secretary Stimson and Navy Secretary Forrestal wrote a joint letter to President Truman, recalling that President Woodrow Wilson had personally chosen "the World War" as World War I's official name. To Harry Truman they recommended "as a matter of simplicity and to insure uniform terminology" the term "World War II." The phrase had been used, they said, "in at least seven public laws [and] has been accepted by common usage." Last week their letter, stamped "Approved" by President Truman, duly appeared in the official Federal Register, henceforth will set usage on all Government documents in the Archives."

"TIME (as far as it knows) was the first publication to make regular use of the phrase, "World War II." TIME began so designating the war in September 1939, when the Associated Press, the New York Times and others were insistently and hopefully referring to it as the war in Europe."

From:

World War II - TIME

And:

[United States, Department of State, Bulletin (Government Printing Office, Washington, 1945), XIII, 427-428.]
10 September 1945
The President
The White House

Dear Mr. President: President Wilson, under date of July 31, 1919, addressed a letter to Secretary of War Baker which read, in part, as follows:
"It is hard to find a satisfactory 'official' name for the war but the best, I think, that has been suggested is 'The World War,' and I hope that your judgment will concur."
Subsequently, under date of October 7, 1919, War Department General Orders No. 115 directed:
"The war against the Central Powers of Europe, in which the United States has taken part, will hereafter be designated in all official communications and publications as 'The World War.'"
As a matter of simplicity and to insure uniform terminology, it is recommended that "World War II" be the officially designated name for the present war covering all theaters and the entire period of hostilities.
The term "World War II" has been used in at least seven public laws to designate this period of hostilities. Analysis of publications and radio programs indicates that this term has been accepted by common usage.
If this recommendation is approved it is further recommended that the title "World War II" be published in the Federal Register as the official name of the present war. [See 10 Federal Register 1188.]

Respectfully yours,
HENRY L. STIMSON,
Secretary of War
JAMES FORRESTAL,
Secretary of the Navy.
Approved: September 11, 1945
HARRY S. TRUMAN

See:

THE NAMING OF WORLD WAR II, SEPTEMBER 11, 1945

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Happy Trails,
Clint.

I've seen publications from as late as 1942 in which US reporters refer to WWI as "The World War" By 1943 it seems like most people had switched to "The Great War" or "WWI"

Churchill seems to have started refering to "The Second World War" sometime in late 1940.

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As my post pointed out the magazine Time was calling the "conflict" which would become WW2 long before it was the "official name", and while Churchill was still out of the official picture. Here is the exact issue, and article. Since the magazine Time began calling the conflict which would become World War II, just that shortly after the first German bombs fell on Polish territory.

"World War II began last week at 5:20 a. m. (Polish time) Friday, September 1, when a German bombing plane dropped a projectile on Puck, fishing village and air base in the armpit of the Hel Peninsula. At 5:45 a. m. the German training ship Schleswig-Holstein lying off Danzig fired what was believed to be the first shell: a direct hit on the Polish underground ammunition dump at Westerplatte. It was a grey day, with gentle rain."

From:

Grey Friday - TIME

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Happy Trails,
Clint.