The y-chromosome does not recombine (at least, under normal circumstances), so typically one would not have markers from all sorts of cultures mixed up into their haplogroup, unlike autosomal DNA (which does recombine). The fact that the y-chromosome is passed nearly unchanged (except for new mutations) from father to son allows us to explore its deep ancestry in a way not possible with autosomal DNA. For example, if I have a son with a Greek woman, he will have a Celtic haplogroup, not a Greek one or a half Celtic/half Greek one.
Your haplogroup does seem to be one that is probably Germanic. It could be Norman, but could also be from the Vandals, Visigoths, or some other tribe. Joining a haplogroup project could help you find your place in the more recent areas of the haplogroup's family tree, which could help you narrow down when your ancestor's line probably came to Italy and where they may have come from.