These are Trench Infantry units, right?
I hope you don't mind a little light reading as my answer.
Our overseas military was called the
Canadian Corps, which refers to the sum of Canadian units fighting overseas during WW1, a total of 5 divisions.
https://en.wikipedia.org/wiki/Canadian_Corps
They were also called the
Canadian Expeditionary Force but that's too long and also refers to all our overseas troops.
https://en.wikipedia.org/wiki/Canadian_Expeditionary_Force
I suppose you could call them
CEF Infantry Battalion, or just
CEF Infantry, since the units raised locally were shipped overseas as numbered battalions.
https://en.wikipedia.org/wiki/List_of_infantry_battalions_in_the_Canadian_Expeditionary_Force
It would be really cool if the these particular units could get numbered in-game similar to how the Scottish Highlander units get named. The third link above lists all the numbered battalions:
1st Battalion, CEF as an example. Just a thought...