Every child I grew up with would refer to them as a **moon bounce**. 

Per [Wikipedia][1];

> They have been marketed with such names as "Bounce House",
> "Bouncies","Moon Bounce", "Boingalow", "Astrojump", "Moonwalk", "Jolly
> Jump" and "Spacewalk". "Brinca brinca" [is] another name commonly used by
> Latinos


  [1]: https://en.wikipedia.org/wiki/Inflatable_castle