Maybe you should check your code a bit... I downloaded the demo and I can play the whole game apparently. After returning to the main menu after the first day, I just clicked on New Game then Skip without entering my name and it sent me directly to Day 2...
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I don't know who downvoted you but yeah, the exact same thing happened to me. I didn't even see your post until just now, after having been fired on day 12. But yeah, I chose new game and skipped the rename part thinking I'd try the demo over again being nasty instead of professional this time and I was on day 2 but with the default name rather than my previous one.