This is called a “Single Wrap Container” or a “convoluted Can”. It’s called that mostly because it is made from two pieces of paper board wrapped around a base. A single wrap you will be able to tell because it will have a seam on the back. If you really want to be generic when talking to a supplier you can just tell them you need a composite paper can and give them your size. It should be able to be made in a few different shapes, but they generally are rounds and squares.
I have attached some info from Sonoco but I would think any of the other big guys would do this and I would also think that most stock packaging suppliers would carry it as well. When doing your search make sure you are looking for paperboard instead of cardboard. You will get much better results.
It made me laugh too. That name is real but it came from a Packaging Engineer that sits behind me. When he told me that I looked at him and said are “you serious?” I always knew it as a Single wrap container.
A convolute can or container is a can that is made through convolute winding instead of spiral winding. It essentially
is a single layer of paperboard that is formed around a mandrel. I have attached a link with info and it will also give you all the info you need on composite cans.