Phoenix Wright: Ace Attorney 6 is heading to Japan in early June - it's definitely coming to the West but, as yet, no release window has been given. We may have an idea of what it'll be called, however, thanks to a cheeky 3DS Homebrew user that made a copy of the recently released demo in Japan.
By dumping the demo a user on court-records.net could see the source file name, which suggests the English name for the game could be Phoenix Wright: Ace Attorney - Spirit of Justice.
The format of the name makes sense, mimicking the naming convention used for predecessor Phoenix Wright: Ace Attorney - Dual Destinies. The storyline also revolves around messages and visions from spirits in what looks to be a mythical turn of events, so Spirit of Justice would make sense.
In any case, it's an indication of what the name might be in the West; hopefully release details aren't far away - based on past form it's likely to be an eShop-only title outside of Japan.
Are you looking forward to Ace Attorney 6, and would you like Spirit of Justice to be its name? Let us know.