I think Fragments is a much clearer, more memorable, easily spelled, and more powerful name. I checked the best known games database and it is not yet being used for any commercial game. I think it stands to provide a more solid foundation for branding the game. That said, I'm not opposed to a subtitle.
The name Fragments is not at all dull. It invokes a question (what is fragmented, why is it fragmented?) and leaves you wanting to know more about it. The game and the design is where the excitement then are created. Magic and Hearthstone both would have to be considered dull as well, but I couldn't agree with that. Magic does have a subtitle, which is why it may be worth discussing subtitles.
There is nothing specifically Cerulean about the game or the fragments in the game. It's a tacked on adjective with no purpose other than to add some color which isn't needed. It adds confusion and makes it more troublesome to write out. It does not add anything about the game and a random color doesn't add more intrigue or more interest.
For the same reasons, I think Fragmented is just as acceptable as Fragments. That said, I prefer a noun, Fragments, over an adjective, Fragmented. I think a noun has a more solid feeling, more tangible, while still leaving the user wondering more. But either way is acceptable.
