I have provided an excerpt below, from pages 1 and 2 of the report, as it presents many of the names by which Okinawa / the Ryukyu Kingdom was known.
The Okinawas of the Loo Choo Islands
A Japanese Minority Group
R & A No. 1567
Office of Strategic Services
Research and Analysis Branch
June 1, 1944
Location: The distance from Kyushu, the southern-most island of Japan proper or Naichi, to Formosa is about six hundred miles and between these two points there is an almost continuous series of groups of small volcano and coral islands, over sixty in number, over fifty of which are occupied.
Names: "The nations of Loochoo call their country Ojiza", according to the "Manchu History". On modern maps the entire archipelago is commonly designated as Nansei Shoto (Southwest Islands). Uruma is another name for the group and the Japanese often call them Nanto Shoto (Southern Islands).
There are five principal clusters or guntos of islands: the Osumi, nearest to Japan; the Tokara; the Amami, including Oshima and Tokuno; the Okinawa; and the Sakishima, which includes the Yayeyama and the Miyako groups or rettos; together with two other very small groups, Sento Shoto far to the north of Sakishima, and the Daito Shoto far to the southeast of Okinawa. The most western island, Yonakuni in the Yayeyama Retto, is only sixty miles away from Formosa.
The name Ryukyu ("Floating Globes") is given to the three southern groups, the two to the north, Tokara and Osumi, being galled Satsunan. The name Ryukyu seems originally to have been applied to Formosa but in the Ming Dynasty was transferred to these islands. In some of the early literature there is often confusion caused by this fact.
Loo Choo is the original Chinese name given these islands. The reading of the same characters in Japanese is Ryukyu.*
*Variants for the spelling of these two names are legion. Some of them follow:
Luchu or Lu Chu
Okinawa, "the land of the extended rope", is the name given to the group (Okinawa Gunto) in which the largest island is also called Okinawa (Okinawa Jima). The same name, as we shall see, was given in 1879 to all the island clusters south of Amami Gunto to form the Okinawa Prefecture. The name seems to have been derived from that of one of the islands called Akonawa on which an envoy of China was shipwrecked in the Tong period. Okinawa was included by the Japanese among the "twelve islands of the South Sea".
Charles C. Goodin