Cage is English. It's a metonymic occupational name for a maker & seller of small cages for animals or birds, or a keeper of the large public cage in which petty criminals were confined for short periods of imprisonment.
Coppola is Italian. It is derived from the Neapolitan term coppola denoting a type of beret characteristic of the region, either a nickname for a habitual wearer of a beret, or a metonymic ocupational name for a maker of such berets. I found this information in a surname book at the library.