It seems impossible to imagine a time before Batman was referred to as The Dark Knight-- but he was about 18 months old before the nickname was first used in the pages of Detective Comics #45 Nov 1940 issue.
Wikipedia gets it wrong, listing the first reference to Batman Comics #1 Spring 1940, there is no mention of Dark Knight in the pages of Batman Comics until #3 Fall 1940 which went for sale on newstands October 19th 1940 and was listed in an ad saying COMING SOON in the very pages of this book indicating it was on sale before the Batman #3.
In Batman #2 Summer 1940 the character is called The Black Knight, but that never stuck.
I poured through every issue of Batman and Detective Comics from the start to locate this information and the book itself will be on display at the Worcester Art Museum's new KNIGHTS exhibit along with Michael Keaton's original Screen Worn Batman suit which opens March 28th!
You'll also get to see the 501st which is New England's branch of Lucas' stormtroopers, music and more-- this will really be an event.