"Miira's Army Cave" is not an official name It may have been referenced in the storyline as such, but has not been officially named. Alternatively, it may be a name popular among fans, but without an official basis.
Miira's Army Cave is a cave in the Kowa Mountains. Miira's Army moved into this cave, into hiding when the group became unpopular and unsuccesful. They waited for a chance to return, until Matoran Hordika found the army from the cave. The army joined her and her friends and the cave was abandoned.
Since the cave is on the area of Kowa, it didn't receive any damage from The Rising. After the Great Migration, some Matoran have moved into the cave.