WASP is an abbreviation for Walter A Sheaffer Pen. Sheaffer started WASP around 1935 or 1936. They originally started the VACUUM-FIL pen company in 1934. I believe it was to test market the new Vacuum-Fil filling system under a separate name to protect the marque in case it did not perform or sell well. It seems to have done well enough for Sheaffer to introduce it in the Balance in 1935.
Soon after, VACUUM-FIL was renamed WASP. Why? I only have more guesses. Perhaps to avoid confusion with the filling system they named Vacuum-Fil and used in both lines of pen. Perhaps because they began to sell lever filling pens under the WASP marque and decided it would be confusing the have a lever filling pen stamped VACUUM-FIL - and such pens exist.
Much like the Parker Vacumatic Junior, the WASP pens came in bolder, brighter and more interesting colors and patterns than their big brothers. Here are a couple of examples.