Should this game have been called "Phoenix," or would that have been a bit too on-the-nose? Maybe, maybe not, since it wasn't clear what remnants or ashes had to do with anything in the game.
If Remnant: From the Ashes needed to be condensed down to one phrase, it'd be "procedurally generated shooter Souls-like," which I think does a pretty good job of covering the game's essential and unique features. I see it as a combination of two twists on the traditional Souls-like formula: the first is making it a shooter and the second is making it semi-random. These are neat ideas with decent execution, but also a few issues.