Nice to know from replies that there is a wide range of different names to call the neck-tube thing! (which I did not know existed before living in Saskatchewan, and now wear every day for probably ~1/3 of the year)
This is the pattern for my favourite one (the one that I need to find...) and it's called a cowl in the pattern! Yet another name! https://www.ravelry.com/patterns/library/sockhead-cowl