Douglas Harper's Etymology Dictionary
1897, from J.H. Salisbury (1823-1905), U.S. physician and food specialist, who promoted it. Incorrect use for "hamburger" traces to World War I and the deliberate attempt to purify American English of German loan words.
Wikipedia
Salisbury steak is a dish made from a blend of ground beef and other ingredients, which is shaped to resemble a steak, and is usually served with gravy or brown sauce. Hamburg steak is a similar product, but differs in ingredients. Salisbury steak was invented by an American physician, Dr. J. H. Salisbury (1823–1905), an early proponent of a low-carbohydrate diet for weight loss; the term "Salisbury steak" has been in use in the United States since 1897. The dish is popular in the United States, where it is traditionally served with gravy and mashed potatoes or noodles.
Usage examples of "salisbury steak".
What you're going to get is Salisbury steak and instant mashed potatoes, a bed-bath from Sister Perpetua, and a whole night of lying flat on your back until somebody remembers that you're still alive and condescends to move you around.
I had a bachelor's icebox: a jar of maraschino cherries, an opened package of Philadelphia cream cheese with fungus growing on it, two tv dinners--Hawaiian shrimp and Salisbury steak--and a tin of condensed milk.
He ate at Jasper's Diner because he liked their Salisbury steak, home fries, and pepper slaw.
I took a tasteless bite of Salisbury steak and thought about how to word my reply.
The second Rob Roy tasted even better than the first, though it didn't exactly complement the Salisbury steak.