Below is a map of Gangwon Province from the 1901 edition of a Korean geography book called Daehanjiji (大韓地誌), which was written by Hyeun Chae (玄采) and published by Gwangmun-sa (廣文社 - 광문사). The map shows "Usan" (于山) as a neighboring island of Ulleungdo (鬱陵島), in a position that suggests that it was almost certainly Ulleungdo's neighboring island of Jukdo. Korea claims that Usando was the the old Korean name for "Dokdo" (Liancourt Rocks), but this map, and many others, is evidence against that claim.
In an 1899 article, HERE, from the Korean newspaper, Hwangseong Sinmun (皇城新聞), "Usando/Jukdo" (于山島竹島) was described as being Ulleungdo's most prominent neighboring island. Korean historians interpret the name Usando/Jukdo (于山島竹島) as being two separate islands, but based on old Korean maps and documents, it is much more likely that the name 于山島竹島 was meant to show that the one island had two names. Notice that "Usando" (于山島) came before "Jukdo" (竹島) in the word combination, which suggests that even if the word combination had been referring to two separate islands, then Usando would have been the larger since it was named first; however, since Ulleungdo's neighboring island of Jukdo is larger than Liancourt Rocks, that still would have implied that Ulleungdo's neighboring island of Jukdo was called "Usando." Besides, can Liancourt Rocks (Takeshima/Dokdo) really be considered a neighboring island of Ulleungdo considering that it is ninety-two kilometers away from Ulleungdo?
In 1900, the Korean government upgraded Ulleungdo's status to a county of Gangwon Province. In the royal edict (#41) that announced the upgrade, Ulleungdo (鬱陵島), Jukdo (竹島), and Seokdo (石島) were described as making up the county. Usando was not mentioned in the edict, in spite of being described as Ulleungdo's most prominent neighboring island in the Hwangseong Sinmun article just a year earlier. The only possible explanation is that "Jukdo" and "Usando" were two names for the same island, and the Korean government decided to make "Jukdo" the official name instead of "Usando." Koreans claim that the "Seokdo" (石島) mentioned in the 1900 royal edict was a reference to "Dokdo" (Liancourt Rocks), but there are no Korean maps or documents to support that claim. "Seokdo" (石島) means "Rock Island," so it is much more likely that it was used as a catchall word to include in the county all the other "rocky islets" that surround Ulleungdo.
Map of Gangwon Province from the 1901 edition of Daehanjiji (大韓地誌)