Has Name your Saves been disabled with this new update? Or maybe it's a joyplay update problem and unrelated.
I think it's unrelated! We didn't change anything in the save system, and I just tested it on Itch.Io and it did indeed let me name my save. I believe someone had a similar problem on the Itch.io desktop app (or maybe it was via Playstation, it's been a while) -- the root cause is that the platform blocked Javascript popups (which is what the named-save function uses).