It is known by a few different common names, including ‘Andean pampas grass’, ‘purple pampas grass’, and simply ‘pampas grass’. ‘Andean pampas grass’ sounds almost like an oxymoron, since the Andes Mountains are in a separate region to the west of the pampas region of Uruguay and eastern Argentina. ‘Purple pampas grass’ is even sillier, since it is devoid of any purple.
I know it simply as ‘papas grass’. That is just how I learned it. The problem with this common name is that it is the same common name of Cortaderia selloana and its cultivars, which is a distinct species that is, on rare occasion, planted intentionally in landscapes. Cortaderia jubata is one of the most aggressively invasive of exotic species on the West Coast, so is not planted.
Cortaderia selloana is safe to plant because it is ‘supposedly’ sterile, so can not naturalize. Technically though, it is not really sterile, but merely exclusively female, without male flower parts for pollination. It reproduces by apomixis, which is a fancy way of saying that it produces viable seed without pollination. No one has bothered to explain why that makes it any less invasive.
Cortaderia jubata reproduces by apomixis too, but makes much more of problem with it. It is very prolific with its unpollinated seed! To make matters worse, it will hybridize freely with Cortaderia selloana if it gets the chance. How does that even work?! Pollen is needed for that sort of hanky panky! Nonetheless, the hybrids are almost as aggressive as Cortadera jubata is!
I just don’t trust any of them. Cortaderia selloana cultivars can work well in large landscapes in urban areas, where they can not escape into the wild. For rural or suburban landscapes that are near wildlands, there are plenty of other less invasive options.