No, i think they said it like that because woojin abandon his name and he become the dead heir's substitute (=・ω・=)
nope, it's the real siwoon who's dead :)
How will Siwoon's mother know that they will swap bodies? .... Phew.... It's not that, she meant that min woojin will live as Min siwoon ... There won't be any "min woojin" for namesake.... Besides the two boys weren't conversive at the least that msw will hear mwj 's childhood story and know who yoon tae min is....
WAIT! DOES THAT MEAN THAT THE REAL WOOJIN IS DEAD!!! (According to the last few pages) I'm confused （/TДT)/
What the hell! Did siwoon and woojin swap bodies as well.....