AutoSaves could not be renamed after storing which was caused by a too long name. The maximum characters the game supports currently out of the box is 25 characters so I had to remove the level name and the player names from the level name and looks now like this:
AutoSave 2022.07.03 0026
Also I added a new option (and renamed the first one) to disable Party & FreePlay games from AutoSaving separatly and can be changed in the BepInEx/config/UCHAutoSaveMod.cfg file with the following parameters:
[General]
## Set to false to disable AutoSave in Party games.
# Setting type: Boolean
# Default value: true
AutoSave in Party = true
## Set to false to disable AutoSave in FreePlay games.
# Setting type: Boolean
# Default value: true
AutoSave in FreePlay = true
Also check out the BepInEx ConfigurationManager with which these configurations can be changed in and while running the game.