When I chose the topic for the game, I had no idea what can the name be. I wrote some versions in the proposal. However, they were just some basic ideas. At some point in the project, there was “verge” and “edge” ideas, late “Sleep Well” appeared. Though they all were questioned and rejected on tutorials. 
From the very beginning, I liked the word “verge”, and it seemed a cool name for the blog. However, it was too long for the actual game. I did a lot of mindmaps, exploring the topic and searching for synonyms.
Some versions:
ReDream Dreamality Ream Dreality Dream vs Reality Dr AlityDeja Vu
I tried comming up with some words: qaistixia
After the next tutorial I’ve also researched some expressions about dreams. 
Tried some things like this:
dream jumble
And some more versions closer to the final one:
dream ли?
in your dreams!
verge of dream
At this point, I started mixing Russian and English. There are some beautiful words in Russian that stand for illusion, nap and other dream related topics.
Some more versions:
omut ( = “wirlpool”)
nayavu (= “in reality”)

The final version was Morok. This Russian word is not commonly used in conversations, it is more of a name from fantasy novels and old poems. It means “glamour”, “illusion”. I do not want to localise this word, to translate it to other languages, so in any language, the name stays the same. I think it sounds beaгtiful and suits the tone of the game.