I have a theory for this name, but as the reason is unclear, the name could always just be what it’s called and there’s no reason to theorise as to why.
My theory is that they don’t want people to know. Perhaps they are called Imagined because they want people to think they’re dreaming when they interact with them. Before C2S5, the Order was all about secrecy, so I wouldn’t be surprised if this is why. But then again, it could just be the name. Either that or the reason hasn’t been revealed yet.
The reason I ask about why is because the other 2 main factions (The Seven and The Last Reality) have reasons for their names (The Seven – Members. The Last Reality – The goal) so with that, I assume the Imagined Order has a reason for their name.