They are labeled on the cans as both Chickpeas and Garbonzo. I just checked my pantry, two different brands both label with both names. I call them chickpeas. Garbonzo makes me think they are like kidney beans, and I hate kidney beans.
I call them chickpeas, but I usually buy ceci as we have a lot of Italian brands in our store. Or, they are kichererbsen - the German name. I have heard of garbanzos, and know what they are, but don't use that name.