What is indoor rock climbing called?

Indoor rock climbing is just called indoor rock climbing. Though, the term could refer to a few different styles of climbing.

Indoor climbing could refer to bouldering, sport climbing, top rope climbing, auto-belay climbing, and speed climbing. Each of these may have similar traits to each other, but they are each different in their own way.

The most common and popular forms of indoor climbing are bouldering and sport climbing. So it is most likely that when referring to indoor rock climbing, it is actually a reference to either indoor bouldering or indoor sport climbing.