Perhaps from a Native American language of the Carolinas such as Carolina Algonquian. If the name was originally applied to a white variety, it could be from the Algqonian root for "white": compare Massachusett wompi (“white”), whence English wamp and wampum.
Meanings
Pontederia species, especially Pontederia cordata.
[…] bulrushes, nut grass, corn grass, switch grass, and the wampees (Pontederia and Peltandra). 1914, American Game Protective Association, Bulletin, page 20:
Pontederia cordata, the pickerel weed, is a member of a small group of aquatic plants usually found in warmer regions of the world. Other common names include dog tongues and wampees. I don't know what the reference to dog tongue is, but the connection with wampees could be the similarity between the seeded pulp of the Chinese […] 2005, H. Peter Loewer, Peter Loewer, Native Perennials for the Southeast, page 155:
Wampee is the Indian name for the tubers of certain swamp plants, […] […] (Pontederia cordata), which occurs in swamps from Nova Scotia to Minnesota and southward to Texas and […] the success they have obtained in hog raising by utilizing the native wampees suggests the possibility of developing a type of agriculture on the old rice lands in which not only native wampees but various other swamp tuberous plants cultivated in Japan […] 1920, American Swineherd: Published Monthly in the Interests of Swine Raising, page 31: