I carry a 20 ounce hydroflask that is always with me. No, it can't be collapsed but I like cold water. Hydroflask keeps water cold for hours. I buy the one with a wide neck so that I can put ice cubes in it. We empty it before security, then fill it in a lounge if there is one we can use. Lounges will have ice. Otherwise, we can fill it at a drinking fountain. Once on the flight, we'll ask for cups of ice to add to it.

I've used a label machine to put my name and phone number on it.