Jin and Sun are married and share the family name "Kwon", which becomes an important plot point in the final season. However, when Koreans marry, the wife never takes her husband's family name. In fact, it is not even permissible in Korea to marry someone with the same family name, except in rare circumstances.
During the 1970s portions, all of the spectacle-wearing characters have an anti-reflective coating on their lenses (the greenish-hued reflection). In the 1970s these were generally reserved for optical equipment lenses.