The Maple Leafs were born in 1927 as the Toronto St. Patricks and played in the Mutual Street Arena. In 1931 they moved to the Maple Leaf Gardens. The History of the Toronto Maple Leaf Hockey Club site doesn’t say exactly, but it would appear that the name of the team comes from the name of that arena.
It may also explain the improper plural form.
Gypsy: Tom, I don’t get you. Tom Servo: Nobody does. I’m the wind, baby.
Looks like Conn Smythe chose the name because he liked it, and named his team and arena accordingly. Maybe he chose Leafs to differentiate between his team and the Maple Leaves mentioned in the quote. BobT, it makes mention of Smythe’s military service, so maybe that’s where your memory is coming from.
There has never been a regiment or battalion in the Canadian Army with the name “maple leaf” as part of its title.
The maple leaf symbol, however, has appeared on Canadian military badges since at least the Upper Canada Militia days of the War of 1812.
Connie Smythe was an officer in the Royal Canadian Artillery in WWI (although he later joined the Royal Flying Corps), and again in WW2 (in charge of the 33rd Light Anti-Aircraft Battery composed almost entirely of NHL stars like Nick Mets, and known colloquially as “the jockstrap battalion.”).