IANAB, but for any ingredients that go in before baking, I think the oven will have nuked any bacteria sufficiently thoroughly for it to be good for 8 hours at room temperature.
I would refrigerate only because the cream cheese could soften. 8 hours at room temp won’t cause salmonella or anything. If you have room, refrigerate.
It’s fine to leave out. If the cream cheese didn’t get soft and runny in the heat of the oven, it certainly isn’t going to from the ambient heat of the house.
Personally, I prefer the texture of a cake when it’s room temp, not cold and stiff, but ymmv.
Once it is cool (1-2 hours), refrigerate. Take it out of the fridge and plate approximately 15 minutes before serving, so it’s not too cold. Put any remainder immediately back in the fridge, as the cooling/warming/cooling cycle is just asking for trouble.
If your kitchen is relatively cool, or you have a cooler room to leave the cake, it’s probably okay until serving, but the best bet is in the fridge.