Word/phrase to refer to things you bring to a place to stay the night?

In a way, it’s a strange thing to remind someone of right after you’ve just told them that they were going to be away for the night. Perhaps it makes sense in some other context, but this sequence seems a bit unlikely:

We’re going on an overnight trip, so don’t forget to bring whatever you need for that night and the next day, since you won’t have the chance to go back home and get it again after we leave.

If you really wanted to, though, I’d probably say not to forget one’s overnight bag. I’ve also heard it called an away bag.

I wouldn’t feel pressed to outline what all I thought they should put in their bag unless it were something one did not normally think to pack, like bug-spray or alternate cell phone or fireworks or rattlesnake antivenin, or even toilet paper if I knew there wouldn’t otherwise be any available where we were overnighting.

I would trust an adult to know what standard things they’d need without coaching. If this were a child without a custodial parent, I would of course be more careful, since children may not be used to packing for themselves.

Given that, you could also say Don’t forget your toothbrush in an informal, somewhat light-hearted way, sort of as a metonym for the whole kit and kaboodle. I have occasionally heard people say that with this meaning.

Speaking of kits, a dopp kit is a genericized trademark for that little bag where you stash a copy of whatever you normally need from the bathroom. Like, well, a toothbrush. It’s the normal word I’ve always heard and used for that zippered little vinyl or leather case, and I was unaware it had any sort of brand affinity.

I suppose you could say toiletries or toiletry kit, but that runs a bit too close to potty training: in American, one often avoids saying the word “toilet” in any context whatsoever. It’s also getting more detailed than seems necessary in an adult context.

I would say "Don't forget to bring your essentials."

According to Google, the phrase "bring your essentials" is sometimes used when discussing packing for a trip.