My old Haven & Belden book reproduces a Colt advertisement and reprints an article from the April 21, 1904 Shooting and Fishing. They show and describe the Colt Officers' Model. Yes, plural, Officers' Model. Not Officers' Model Target... yet.
The ad is headed "The New Colt Revolver" and subheaded "Officers' Model."
It reads: "This is our New Army Revolver, caliber 38, with special additions and improvements as noted. This will be found a superior weapon for target practice, with service loads or with reduced charges, round or conical ball" "Target Sights, Front Sight Adjustable for Elevation. Rear Sight Adjustable for Windage." "Selected Walnut Stocks, Finely Checked. Guard, Strap, and Trigger Finely Checked. 6-Inch Barrel, Blued Finish."
Then there is a reproduction of "A page from the Colt catalogue for 1905." for the "Officers' Model Target" with description similar to the 1904 literature, but with "Target" added to the model name.
The action was upgraded in 1908, according to Haven & Belden, but general features and model name stayed the same until the time of the book in 1940. By then there were more choices in barrel length and caliber.