He announced it in an interview and made it official through Fancafe (the Korean Weverse, if you didn't know).
Key questions from the interview that made him known:
X:If you could say something to your younger self, back when you first started the band, what would it be?
RM:Please change your name! Please change your hair and put away those sunglasses.
X:RM, you mentioned changing your name, what does "RM" mean to you?
RM:"Rap Monster" came from a song I made in 2012. There was a line like "Rap Monster," and I just thought it was cool. But as I grew up and when I came to the United States, I thought it was too much. So I shortened it to RM, and it could symbolize many things; it could have more meanings.
X:What does it mean to you right now?
RM:I don't know, like "Real Me" or something like that.
While it's a change that took time, they look back on the past fondly because, after all, it's part of their history. Even today, the rest of Bangtan still mistakenly call him "rapmon", a simple affectionate nickname.