"Hash browns” (or “hashed browns") were originally called, in full, “hash(ed) brown potatoes.” They are cited in the New York World in 1888.
(Oxford English Dictionary)
hash browns chiefly U.S., = hashed brown potatoes s.v. HASHED ppl. a. b; more fully, hash-brown(ed) potatoes;
1917 I. C. B. ALLEN Mrs. Allen’s Cook Bk. 400 *Hash Browned Potatoes. 1948 H. L. MENCKEN Amer. Lang. Suppl. II. 388 Of late there has been a strong tendency..to omit the -ed ending… Examples: mash potatoes, hash-brown potatoes, [etc.].
November 1888, Current Literature, pg. 402:
Lunching With A Man. New York World
Scalloped chicken, with hashed brown potatoes, lobster salad and two chocolate eclairs, were destined to pass before his agonized stomach before a halt was called and the girl with the delicate appetite had proven her lack.
30 November 1892, Indiana (PA) Progress, pg. 7:
Mrs. Rorer gave her audience a shock the other day while lecturing at the Health and Food Exhibition in New Haven, Conn., by prophesying dire disaster as a result of indulgence in “hashed brown potatoes.” She had visited insane asylums, she said, and found that many of the inmates had been addicted to the use of potatoes fried after being boiled. Ergo, potatoes cooked in this way appear to produce insanity.
28 January 1894, Los Angeles Times, pg. 24:
He is fond of cold ham and turkey, and one of his side dishes is usually hashed brown potatoes served up with a poached egg upon them.
28 December 1895, Fort Wayne (IN) Evening Sentinel, pg. 4?:
“I’d trade it for a porterhouse steak and some hash brown potatoes.”
(Writer Eugene Field—ed.)
20 December 1922, Fitchburg (MA) Sentinel, pg. 4:
A spud raiser may be down, but he is never out, apparently, and the epicureans are helping out all they can by intensive orders for hash browns and a la Delmonicos.—Malden News.
25 April 1926, Modesto (CA) News-Herald, pg. ?:
Sometimes, dog tired, he dropped off his engine in the yards, cleaned up at a pump outside the station and are pork sausages, hashed browns, coffee and sinkers at his mother’s supper counter before they both cut home through the stubble of sage brush between the station and the one-story shack.