Because we're Korean. :)
In all seriousness, it's a Korean tradition. Here's a part of a Wikipedia article about it:
"Korean women keep their family names even after their marriage, but their children take the father's surname.
In the pre-modern, patriarchal Korean society people were extremely conscious of familial values and their own family identities. Korean women keep their surnames after marriage based on traditional reasoning that it is what they inherited from their parents and ancestors, and cannot be changed. According to traditions, each clan publishes a comprehensive genealogy (jokbo) every 30 years. However, it is not uncommon for women to be addressed with their husband's surnames after marriage.
There are around a dozen two-syllable surnames, all of which rank after the 100 most common surnames. The five most common family names, which together make up over half of the Korean population, are used by over 20 million people in South Korea."