The following record talks about the appointment of two inspectors tasked with going to Muleungdo (Ulleungdo) to bring back people hiding on the island. On February 8, 1437, King Sejong had talked about sending people to Muleungdo, so the selection of these two inspectors was probably the result of that.
Source: 『世宗實錄』 卷 八十一, 世宗 二十年 四月 甲戌條
April 21, 1438
以前護軍南薈 前副司直曹敏 爲茂陵島巡審敬差官 二人居江原道海邊者 時國家聞茂陵島在海中 多産異物 土沃可居 欲遣人尋訪 而難其人 乃募於海邊 此二人應募 故遞授敬差官之命 以遣 仍使搜檢逃匿人口
전 호군(護軍) 남회(南薈)와 전 부사직(副司直) 조민(曹敏)을 무릉도순심경차관(茂陵島巡審敬差官)으로 삼았는데 두 사람은 강원도 해변에 거주하는 자이다. 이때 국가에서는 무릉도가 바다 가운데 있는데 이상한 것이 많이 나고 토지도 비옥하여 살기에 좋다고 하므로 사람을 보내 찾아보고자 해도 그 사람을 얻기가 어려웠다. 이에 해변에서 이를 모집하니 이 두 사람이 응모했으므로 경차관을 제수하도록 명령하고 파견하여 섬에 도망하여 숨어있는 사람들을 수색하여 오도록 한 것이다. 이에 도망해 숨은 인구도 탐문하여 조사하도록 한 것이다.
Former hogun Nam Hoi and former busajik Jo Min were assigned as "Muleungdo Inspectors." Both men live on the coast of Gangwon Province. Muleungdo was then known to be in the middle of the sea and was said to be a good place to live because it had fertile land and many strange products. Even though we wanted to send people to search the place, it was not easy to find people to do it. Therefore, people were solicited from the coast and these two people were recruited. They were given the title of "inspector" and sent to the island to search out and bring back people hiding there. They also were supposed to investigate and determine the number of people hiding there.
On August 8, 1425, Kim In-u was made "Inspector for the Usan-Muleung Region," but notice that in the above record Nam Hoi and Jo Min were given the title of "Muleungdo (Muleung Island) Inspectors." This could mean that the main island of Ulleungdo was being called Muleungdo, or that Muleungdo was being used to refer to the island group (Ulleungdo and its neighboring islands). Based on the fact that the main island of Ulleungdo has also been referred to as "Usando" (See 1412, 1417, and 1436), I tend to believe that Muleungdo was being used as a general reference to the island group. Also, Kim In-u had previously been called the "Usan-Muleung Regional Inspector," which suggests that Usan was the larger island since Usan came before Muleung.