You'll likely see it romanized, using a combination of Korean consonants and vowels to approximate the English pronunciation. Different people might slightly vary the spelling. A common approach would be something like:
* 매디슨 (Maediseon): This is a relatively straightforward transliteration based on pronunciation.
Keep in mind this is a romanization, not a true translation. There's no inherent Korean meaning attached to this spelling. If you wanted a Korean name *with a similar meaning or feel*, you'd need to find a Korean name that evokes similar imagery or qualities (e.g., elegance, strength) rather than attempting a direct translation of "Madison."