The Red Rainbow Fish, Glossolepis incisus, typically has more, or less red on its body with age and to a certain extent, mood. There is a strong sexual dimorphism as well, males retain far more pigment cells into maturity then females, which are at best yellowish at full size. Even full grown males, (150mm/6"), can, in quality specimens, turn deep red.
These are social fish best kept in group, if you have just one, it may never show it's best colour. Alone, they stress.
I suspect the common name you gave derives from it's original home, Irian Jaya.