Responses
Im pretty sure that in one of the beginning chapters it talks about how he really wanted to go to high school. So if he wanted to go to highschool and his brother wanted/ was willing to go abroad instead, they couldve switched places. Thinking from a logical standpoint: they probably wanted to hide this switch from everyone. (Except that Hangyum gave Hajin his real name for whatever reason, probably hoping to start their relationship again). Thus they took on each others names and place swapped. Once they switched back however, they would have to keep all of this hush hush, hence lying about going to school.
For real I wonder what crazy reason he could have for pretending to be his brother. Obviously he was the one who went to high school with Hajin. #BLLogic