A new cultivar of Hydrangea, Hydrangea paniculata ‘RENHY’, characterized by its large panicles of sterile flowers that emerge white and change to pink and finally to a red with maturity with the red coloration lasting about 3 to 4 weeks, its continuous flush of new flowering stems that give an overall multicolored effect in late summer to early fall, and its plant habit that changes from erect in early summer to cascading as the season progresses.