The chapters with the Korean names are chapters that were done by translation teams. The creator of the manhwa saw how popular the comic was and released it in English on the site Tapas. There the names were changed. I guess it was done so readers who weren't used to Koreans names wouldn't be confused and have to keep on guessing who was who. I haven't read the new chapters but I assume they were grabbed from Tapas which is why there is a name switch.

This is kind of like lookism (name wise) they change the Korean names to English sounding;; why? I got so confused who Justin and Edward when I looked into the comments were so I peeked into the very last chapter, to see if it says anything about it, I’m not finished yet (still reading) but do they have a reason for changing the names? does it kinda just happen to appeal to international fans?