I've seen these called oyster baskets and clam baskets but I grew up knowing these as egg baskets. My grandparents lived on a farm in Iowa and we'd visit them a few times a year and this is what we used to collect eggs from their large flock of chickens.
I've had one of these baskets for years, the rusty one. The house we moved into when I was 11 in New Jersey had an old time junk yard in the back of the house in the woods where I found it and many other 'treasures' that I still have today. The basket has moved around from place to place with me and was in the basement for years until I recently decided I could use it for storage in my bathroom. It seems that utilizing different things to maximize space in my home is an ongoing theme. We recently found a second basket at an antique store for a good price and snatched it up to compliment the old one.
I hung the baskets with a couple screws, nothing fancy, and we'll be using them for towel storage and whatever else will fit in their odd shape. I'm hoping to find a rectangular wire milk crate to hang next to the baskets eventually.