When you move the wah pedal, you're moving the cutoff of the filter, not the Q. The Q is fixed.
You're also incorrect about the name. Just 'wah' is perfectly acceptable.
https://en.m.wikipedia.org/wiki/Wah-wah_pedal
Because of the Wha-Wha (or Wa-Wa) effect.
Shopping online it looks to me like “Wah pedal” is more popular than “Wah-Wah pedal”. Here’s a pile of examples of guitarists using “Wah pedal”: https://www.sweetwater.com/c976--Wah_and_Filter_Pedals https://www.guitarcenter.com/Wah-Filter-Effects-Pedals.gc https://www.guitarworld.com/features/best-wah-pedals https://www.bestreviews.guide/guitar-wah-pedals https://www.musicradar.com/news/the-best-wah-pedals
"A wah-wah pedal, or simply wah pedal"
this is just not true. guitarists regularly call it either. i hear it called a “wah” more often these days than “wah-wah”.
anyone will clearly understand and not look at funny if you say “wah pedal”
[1] And it has to be a “wah-wah”, not “wah”.