When asked where the name Ween came from, Dean and Gene often say it's just a word they came up with as teens that they thought sounded kind of cool. Aside from just the band name, Dean has also stated that this is how many album and song titles are named, for example, they wanted to go for a Beatles-esque sound on their White Pepper album and Dean claimed "White Pepper" sounded like a classic rock title, so the album's title references the Beatles' albums The Beatles (commonly known as The White Album) and Sgt. Pepper's Lonely Hearts Club Band.
Deleted this interesting example listed under A Good Name for a Rock Band, which it no longer fits: