Yeoui-do (여의도) is written with the following hanja:

汝矣島

The first one, 汝, means "you," 너 in Korean. The second character is used in Chinese literature as a particle that indicates a change of state, and can usually be rendered "..., now." It is read 의, and is borrowed for the sound of the possessive marker 의 in Korean. The two characters together were read 너의, or your. Together with the 도 for island, 여의도 means your island.