Is there any new content or is the game just renamed?
It's basically just a rename.
The story has been slightly modified, but as far I could tell the only real change in the story was that they removed Paul (the father) from the story entirely, and the handful of scenes that he was in have either been removed or modified so they are now featuring Eve instead.
It also has a new User Interface design, which looks quite good and professional in the menu's. In-game however, I personally preferred the old user interface, especially when it comes to the dialogue box. The old in-game interface was more minimalistic whereas the new one is very present.
The biggest and probably best change is that you can now disable the freeroam aspect of the game, and disable the mini-games (which I believe were also a new addition to this new version). With the freeroam disabled, the game plays like a more traditional VN where you just have to make choices. During my playthrough however, I still encountered several moments where I still had to do some minor freeroaming even though I had it turned off, but I'm assuming that was a bug. Although a welcome change, I never really minded the freeroam in "Red Falls" that much either, since it wasn't as tedious as it is in many other games.
When it comes to render quality, I didn't notice much of a difference with this new version. But, I do play on a 1920x1080 screen, so you might see big improvements if you play on a 4k screen.
Based on the fact that the changes are mainly cosmetic and the story is essentially exactly the same except for the fact that they cut out Paul / the dad from it, I don't really see the reason for the name change. When it comes to the name I actually preferred the previous, less generic name "Red Falls" over the new one.
Game is still good though and a lot of fun to play.