The term for a communal courtship arena where males display to females is a lek.
In a lek mating system, males gather in one area and perform competitive displays—such as calls, dances, postures, or wing movements—while females visit and choose among them. Males usually provide no parental care; their main contribution is fertilization.
Leks are especially associated with birds such as sage grouse, black grouse, manakins, and birds-of-paradise, but the behavior also occurs in mammals, fish, amphibians, reptiles, insects, and other arthropods. A classical lek has males close enough to see and hear one another, while an exploded lek has more widely spaced display territories.
A common mix-up is treating a lek as a colony or rookery. Those terms describe a living or breeding aggregation, whereas a lek specifically centers on male display and female mate choice. The word can refer both to the gathering and to the display site itself.