According to a 1948 citation, the dish was invented at the Drake Room, at 56th Street and Park Avenue in Manhattan's Drake Hotel, and was named after Chef Beniamino Schiavon's small daughter.
Wikipedia: Steak Diane
Steak Diane is an American dish of a pan-fried beefsteak with a sauce made from the seasoned pan juices, generally prepared in restaurants tableside, and flambéed. It was popular in the middle of the 20th century, and became considered dated by 1980.
"Steak Diane" does not appear in the classics of French cuisine, and was probably invented in mid-20th century New York as part of the fad for tableside-flambéed dishes. The name 'Diane', the Roman goddess of the hunt, has been used for various game-related foods, but the "Venison Steak Diane" attested in 1914, although it is sautéed and flambéed, is sauced and garnished with fruits, unlike later steak Diane recipes, so it is unclear if there is a connection.
By the 1940's, Steak Diane was a common item on the menus of restaurants popular with Café Society, including the restaurants at the Drake and Sherry-Netherland hotels and The Colony. It is often attributed to Chef Beniamino Schiavon 'Nino of the Drake'.
1 October 1948, Washington (DC) Post, "Gotham's Famed Chefs Cook for Food Editors; Food Editors Dine on Gay Nineties Fare" by Lucia Brown, pg. C1:
EARLIER in the week, a smaller group of us was entertained at a gourmet dinner hosted by a baby food company in the Drake Room on 56th st. at Park ave. This is a spot that has become famous among New Yorkers for its buffet luncheons, as well as for such dishes as steak Diane. This was made for us by Nino, the maitre d'hotel, who created the dish and named it for his small daughter.