Passing Into Fantasy - I like the "Fantasy" part, it goes well with how the game looks like. However "Passing Into" isn't very snappy... I would choose just one extra word to make it sound more catchy... like "Terminal Fantasy"
Soul Runner - I don't know, to me the "runner" thing doesn't have much of a sound and it's been used up. Same kinda goes for the "Soul", but that's kind of a "special word with a deep meaning", so it's still useful to create "instant atmosphere" (just add hot water). I'd mix it up a bit. Maybe cut the "ner" and just make it a Soul Run (and add hot water). Still, not sure if it's powerful enough to create an impression.
Also some more creative stuff comes to mind, like "Soul for a horse" (would be cool if the game involved an actual horse at some point) or "Devil's appetite".
Soul Prison - Another "Soul" one, heh...

"Prison" to me sounds more interesting than "Runner". But looking at the screenshot, I'm not sure if there is a soul involved . Nor a prison for that matter.

I guess it goes with the narrative of the game, which is ok I guess, but it could be better to work in the actual gameplay into the name. Something like "Clash of Souls" (that's cheesy though) or "Pressed Escape on Myself" (thats too...
meta 
xD).
The Ouroboros King - I know it's a word from the actual real-world mythology, but it just sounds... terrifying.

By which I mean that noone will ever want to say the word "Ouroboros".

Something simpler might be better (eg. "Mythos Kings" / "Eternal Kings"... bit uninspired but you get the idea).
Kingdom of Atham: Crown of the Champions - To me, "Crown of the Champions" sounds like a sub-title of a B quality 90s fantasy movie.

(although it would probably be without "the", ie. "Crown of Champions")
(Honestly I wouldn't recommend sub-titles for game names in general unless you have a reeeal good reason to have one.)
I don't mind the Kingdom of Atham though. I get that without the sub-title it kinda lacks a twist though. Maybe just squash the whole name into a smaller one - like a little cheesy "Kingdom's Champions" (variants: King's Chosen, King's Best etc), or more epic "Crown of Atham"...
EDIT: haha now I read Gunroar:Cannon() made the same suggestion before me, oops.

I do like that name tho, and I think it would look cool in that font of yours as well.
Idle Party Leader - Sorry but this just evokes "party (cheer)leader". Especially in the logo that I saw where the "idle" is a little sideways and much smaller, while "Party Leader" is written in a uniform font.
I would have
never guess that it's about politics and not some "paaartyy".

I do like the "Idle Leader" thing tho. Maybe just leave it as that? You don't have to use a political word for people to understand. Especially with a modern word in the title ("IDLE"), the "leader"should be enough (after all, politics are by definition about how the people govern themselves, or how are they "led" - the whole thing kinda requires some kind of leaders, xcept for some specific movements where
everyone is a leader).
Some different approaches come to mind too. "Political Animal", "Candidate", "Senate Road", "History by Victor", "
I wish I was a president", "State of my state", "Shepherd's tie"... done for now.
Unfair Dash - First of all, I don't think it's wise to call game "unfair". It's ok to make a difficult game, but the player must never feel that it is
unfair (and this is actually only partially connected to difficulty, it's more about how the game presents the difficulty).
I do understand though that you want to tell people that the game is difficult.
I think you should not. There's a million of ridiculously difficult games which are difficult because they are too hardcore, too raw. This kind of difficulty is actually nothing to advertise. And nobody actually cares about it either. You're just telling players that your game is going to frustrate them, and more importantly, that you have nothing else that is interesting/original enough that you could tell them about it.
If it is truly hardcore (and from the looks of it, it is not hardcore enough to be called that, at least in my opinion), or even when the difficulty lies in something else (logic, for example), you still don't want to use the word "unfair". In the end it's best to be creative anyway - one of the more visible hardcore games of the last years, an actual satire about hardcoreness in games, wasn't called "Unfair Mountain", it was called "Get Over It."

Maybe focus on unique aspects rather than the fact that the game is difficult to jump through (everybody understands that already anyway when you call game a "Dash" - which might be generic word, but I actually think it fits).
How about naming it so it's clear what is actually special about this dash? (There are lots of dash games out there) I can't say much from the screenshots you provide on your site, but to give you at least some idea of what I mean: Cube Dash, Dash & Smash, Rope Dash... considering your narrative, maybe Prison Dash, Hell Dash, Monster Dash, Dash of Freedom (not very original examples but you get the idea)... or you may go more creative with it and come up with something like "Dash of Mischief"

The goal is to have name that is special because it says why your game is special.
(Obviously you also want the name to be easy to remember. "Dash" as a short generic word should be good for that, but the other word should be less generic, otherwise your game will get lost in the sea of similar dash games.)
Shadow of the Orient - Ok I'm going to have a little issue with that... xD
One note would be that "Shadow of/over something" is a little used up and lazy form (btw "over" sounds better than "of"). But thats fine, "shadow is a cool word" and all that.

But "the Orient" part... first of all, I'm not a native-speaker, but with that "the", to me it sounds like "Shadow of the Europe" instead of "Shadow of Europe", just... wrong, I don't know.
Grammar aside, the only thing the name really says is where it is set - in Orient. Which is, originally, a name for Middle-East and Middle-East only. Looking at your game though, that is not Orient. (
This is Orient [indie game]) Backgrounds fit a little, sure, but man, in the very first gifs you have a Buddha statue there... that's a
very wide understanding of the Orient.
You can say "well I take the most recent most wide definition of the word", but then you are defeating the purpose of the whole word: to tell players where it actually is set. Right now it basically looks that it's set "anywhere", making the "Orient" in name pointless, making the whole name say... nothing about the actual game.
Most people will feel this when reading the name and it will make them forget the game.
It's ok to use "Shadow" because it sets the mood. But don't name your game based on it's location (especially when the location actually isn't
precisely correct), that makes sense only when you're
recreating some real and actual places (like Damascus, or Babylon) or when you are referencing a well-established world (like Tolkien's Middle-Earth).
Instead, focus on what the player actually does in the game.
Are we fighting the shadow? Are we running from the shadow? Are we becoming a shadow? I'd be much more interested in the game if it was called "Shadowraid". Or Shadow and sand / Sand and shadow, or Eastern Knights (Eastern Nights?) or Bamboo warrior, if you really need to reference Asia.

(If you really need the keyword, you can put "orient"/"oriental" in the game's description.)
(Note: I am only discussing the name and how it fits the game world - the game itself looks well-made and very polished, and so does the website, nice job.

)
@DarkGran - Save Me Circles: At first I read the name as "Save the Circles" which was really generic, but then I checked again and that name's more unique though it's still weird because why is what being saved...? Though it could still work maybe a name that includes the goal of the game in some way like "One Circle At A Time" or "Color Me Circle"?

(Honestly I don't know about those cheesy names XD but you get the idea). Like the unique puzzle idea.
Haha I actually find those names real fun and not cheesy at all! Might actually use something along the lines.

Also thanks for pointing out that at first you've read the name differently. This is something that happens to people a lot and it is something we should watch out for when naming games, because often people won't read the name again (unless what they actually read sounds really strange, then they will "make sure"), and even if they do, the power of name is somehow diminished, which always hurts the game... I will call it "
clarity of the name".



Funniest example of mine is probably my "serious sci-fi" game's name Farstar read as Fart-star...

Cheers!
