In Greece itself, it is simply "salad" or "country salad."
The following citations indicate that it was popular in delis and restaurants from the 1910s.
7 June 1910, Seattle (WA) Daily Times, "The Manicure Lady on Linguists," pg. 12, col. 5:
"Then he calls over the Spaniard and said something to him in Spanish that meant a steak, but sounded like water dropping on a hot stove, and when it came the Greek's turn he ordered a Greek salad, talking Greek that must have been the real McCoy, be4cause the Greek nodded his head.
4 July 1914, Fort Wayne (IN) Sentinel, pg. 27:
They had Russian cabbage soup, Hungarian goulash, Greek salad, Italian macaroni, German pancake and Turkish coffee.
(The story is by Israel J. Zevin and was originally published in the New York Herald -- ed.)
The Lunch Room as a Money Maker
compiled by C. A. Patterson
Editor and Publisher of the
AMERICAN RESTAURANT MAGAZINE
Chicago: Patterson Publishing Co.
Pg. 79 ad:
The Odenbach Delicatessen
Announcing Friday Specialties
for Your Home Table
Here you can obtain pleasing delicacies to arouse the family appetitie on "Meatless Days" -- both economically and well.
Crab Meat Salad
Cold Salmon with Mayonnaise
Soft Shell Crabs
4 September 1922, New York Times, pg. 8:
Rabeles's Sunday dinner patrons are fond of roast chicken and roast duck. A Sunday dinner on Second Avenue is not complete unless it begins with chopped chicken liver, chopped herring or Greek salad, marked on the menu as "appetizer."
18 April 1923, Chicago Daily Tribune, pg. 23:
WINNIE WINKLE, THE BREADLINNER:
Better Add Pork and Beans, Winnie
WE'LL START WITH RUSSIAN CAVIAR THEN SCOTCH BROTH, SPANISH MACKEREL, ENGLISH MUTTON-CHOP, GREEK SALAD, ITALIAN SPUMONI, FRENCH PASTRY AND TURKISH COFFEE.
An Autobiography of Greek Travel
by Kenneth Matthews
London: Peter Davies
Salads and Herbs
by Cora, Rose and Bob BrownJ.
Philadelphia: B. Lippincott Company
Three parts shredded raw vegetables--cabbage, carrots, green pepper and onion. One part smoked herring, diced. Thin mayonnaise with sweetened vinegar, add and mix thoroughly. Pile on lettuce leaves.
19 April 1941, New York Herald Tribune, pg. 10, col. 6:
Roast lamb, almost without exception, will feature at the Greek Easter Sunday dinner. Potatoes will brown and sputter in the fat of the roasting pan. Greek salad substitutes for vegetables made as it is of radishes, green onions, tomatoes, lettuce--all dressed cozily in a film of good oil. Most dinners will take off with the national soup, maghiritsa, the stock for this made with the liver of the lamb, and the intestines cooked together long and slowly with dill in the water. A sauce made with cream and the yolks of eggs thickens the soup.