The Chinese used the term Ryukyus in many documents over the course of history. The currently used Chinese characters for the Ryukyus came into use when King Satto of the central Chuzan Kingdom established relations with Ming China in the 14th century.
The current Chinese characters used to designate the prefecture Okinawa came from the name the local people called their own island (Uchina in Okinawan dialect). It was first used in documentation in Japan in the "Tale of the Heike" by Nagato.
There are some historians and who believe the first historical use was a place called "Aji-Naha-to" in the "Todaiwa Joto Seiden." There are also references to Okinawa as "Akina" as well.
The name Okinawa can be found in documents from the Shimazu domain in the 17th century and in Arai Hakuseki's "Nantoshi". In this book Okinawa is written with the current characters and it is therefore said to have been in common use.
When the edict dismantling the Ryukyu Kingdom was issued and the domains were abolished, the prefectural system was established and the Ryukyu Domain was named Okinawa Prefecture because the name Ryukyu came from the Chinese.