My dad was with the 34th ID also - even though he was a Georgia boy and the unit was originally Iowa, mostly. They wound up with all sorts of people from all over as the war progressed.
Dad's unit was the 109th Combat Engineer Bn. He was at Anzio (but didn't go in w/ the first wave), then they went up the Italian mountains in the winter of 43-44.
I'm no expert, but from what I understand the National Guard divisions lost their local flavor pretty quickly in WWII, as replacement troops came from all parts of the country -- especially into units with high casualties.
The 34th ID has a very proud legacy (and the legacy is still going on today).