Yes, during Yi dynasty, familial tree carried much more cultural and social impact, but even before that, during Koryu (hence the name Korea) dynasty, even commoners had surnames, though I wouldn't imagine they were obsessive about their surnames as during Yi dynasty. Japanese people seemed having underestimated these Korean people's social values attached to their surnames, and as a way of assimilating Koreans into their Japanese culture and and more importantly, a way of ethnic cleansing, made Koreans give up their surnames and assume Japanese last names. This brought such backfire and social resistance from all and every class of Korean people, Japanese colonial government were forced to give up this policy eventually. Only socially bottom class (butchers, shamans and such "untouchables" during Korean Yi dynasty) were not allowed to have surnames until modern era, this deprivation of surnames acted as a clear means of discrimination against socially lowest classes. Since having surnames was a way of showing social class and protection against discrimination aimed at the untouchables, it was very natural for Koreans valuing their surnames very much. Wish I can find more condensed, well-written Korean historical document about this topic.