I've seen all three versions for describing a person on stage performing comedy: "stand up", "standup", and "stand-up".
My guess is that the term started as two words, but as the performance form itself became more established in the culture, the set of the two words together became perceived as a single unit. Reflecting that, in writing, some people even started merging the words or joining them with a hyphen.
Based on that assumption, I'm extrapolating that it's a term in the midst of evolving, and so maybe there might not be an absolute answer on this.
Still, I'd like to be consistent myself and settle on one. Is there any particular reason I should choose one over the others?