(DISCLAIMER!: I don't know if someone has already made a theory about this, I just joined this community like two days ago and this is my first post. If someone has already made a theory on this, I'm sorry if it seemed like I stole your theory. I just wanted to make a FNaC theory. With that being said, let's hop on into the theory.)

The RAT is one of my favorite animatronics in the FNaC franchise.

In FNaC 3 where Mary is hiding in the closet of 'employees only' room, the player can look around at items and such, one of them being the script for the 'surprise show'.

In the script it is said that they would reveal the CAT and RAT's real names, and revealed the CAT's real name to be 'Candy', while the RAT's real name is not revealed (because for some reason Mary didn't read that part of the script?)

I have a little theory that the RAT's real name might or might not be 'Randy'.

To be honest, it kinda fits in my opinion, with both of their names rhyming which would be pretty cool, but the mystery of the RAT's name being hidden and unknown adds the eerieness to the character.