"Tommy Atkins" as a generic name for British soldiers goes back at least to the 18th century (a letter of 1743 is cited as the first use) , but it gained traction in the 19th when the War Office chose it as the generic name for example forms in the Soldier's Account Book.
Various "original Thomas Atkins" es have been suggesed over the years, usually a soldier noted for some act of bravery and noted by the Duke of Wellington or some other worthy, anywhere between the Peninsular War and the Indian "Mutiny".
In 1898, Rudyard Kipling published a collection of "Barrack-Room Ballads", which included a famous poem "Tommy", which calls out the way that soldiers are popular when there's a war to be fought, but shunned when back home.
Yes, makin' mock o' uniforms that guard you while you sleep.
Is cheaper than them uniforms, an' they're starvation cheap.
An' hustlin' drunken soldiers when they're goin' large a bit.
Is five times better business than paradin' in full kit.
Then it's Tommy this, an' Tommy that, an` Tommy, 'ow's yer soul? "
But it's " Thin red line of 'eroes " when the drums begin to roll
(As an aside, Scotland's greatest bard, William Topaz McGonagall - not a man noted for his subtlety - missed the point of the poem entirely and published In Praise of Tommy Atkins. Connoisseurs of dreadful poetry will enjoy some time perusing his works.)
Anyway, there were a number of similarly high-profile pop-culture references to Tommy Atkins the British soldier during the 1890s and during the Boer War, so it was firmly established by the time WW1 rolled around.
Edit: Sources
Ivan is one most common Russian and Slavic names, which also is not really used elsewhere. Fritz is a common slang for a German male I have read. As well a common name male name,.
The person below saw give nice background on origin of 'Tommy'. Which was used a much in 1st world war. I did not know dated that far back, only was aware of Tommy Atkins. Guess where 'the Who' got name Tommy for one their albums now that think about it
I was just listening to audiobook of a German solider fighting in east in WWII. 'Ivans' was the word he always used for the Soviets/Russians. It was the most used word in the book by quite a large margin. Figure it would be a lot like calling Americans Smiths or Johnsons or Chinese Wangs or Changs