Nomenclature aside, do you confirm that the vowel in Ciocc is pronounced like the German umlauted o?.
The name is simply nonsense as explained by the originator (who it should be noted is no longer the owner of the brand!) so trying to determine what influenced him seems pointless. The pronunciation of the whole name is definitely not German and your average German would not have any idea as to how to pronounce the combination of letters. It is a bit like Häagen Dazs, it is simply nonsensical but does evoke a certain feel. You would hear many different pronunciations if you presented the name to your average German. I can't think of any German word that combines iö. Furthermore to get the pronunciation accorded to it by Pelizzoli, in German you would likely need at least an S following the ö. The pronunciation of the ö does however seem to follow what your average Italian would be taught as being the way to pronounce the German ö.
...perhaps we are confusing political and linguistic borders. I think it would be fair to say that part of (political) Italy is near the (linguistic) German border, and some of it (South Tyrol) is even on the German side of that border.
As regards the linguistic situation of Bergamo, I am not very well-informed but do believe it is fair to say that the city of Bergamo has never been part of the region of German language influence, but that it has likewise been under Germanic rule at some time in its long history. Perhaps some of the very outlying Northern parts of the province of Bergamo might have felt a bit of influence of the German language but not the city. Typically, influence radiates out from the cities outward in Italy and not the other way around and there are some major physical barriers (lakes and mountains) between Bergamo and the areas of German language influence.