Since many people are also confused about Mugo:
No, there is no "main Mugo" they are all Mugo. However the don't have the same role in the system, meaning they don't have the same powers.
Glasses Mugo is a protector and a host, that's why he has more power over Mean and Monster. He needs to control who is in front, and only fails when the trigger is too strong.
Mean Mugo is a persecutor. He's trying to protect them by being rough. He also suffers emotionally from decisions made by Glasses Mugo because he disagrees.
Monster Mugo is akin to a child, he probably is a childish personality in the form of a monster in their mind, but appears as Mugo/snake because that's what the body physically is.
The 4th Mugo is a trauma holder and a host. As a trauma holder, he fully remembers the trauma that let them there, including memories that could be fuzzy/forgotten by other Mugo's. He is also a host, and because he is also a trauma holder, he recognized the MC from their past life, unlike the others who don't fully understand the situation. He is also a host, and probably a protector.
The fact that the other personalities don't know about him gives him the power to appear without their knowledge. Their dissociation comes with memory loss, so they don't necessarily remember what the others did, and sometimes, if another personality takes over forcefully, they don't know which personality. And because of the memory gap, they don't even know.
Usually people with dissociative disorders that include memory loss can tell there's an issue because people around them tell them what they did or things were moved. In this case, Glasses Mugo couldn't tell because there was no clear indicator and he genuinely thought there were only 3 of them.
You are welcome.
My prediction: MC is a reincarnation of the Mugo's lover, the sacrificed family probably killed the lover, which traumatized the Mugo and caused the dissociative disorder, and the 4th Mugo recognized their lover and saved him from being eaten.
Now we're gonna have a story of the MC's journey to discovering that, then troubles, then him living happily with Mugo. (Or, if tragic ending: dying or Mugo disappearing of both).
That's it.