The word "Italia" dates back to before Rome was not even a town. It used to be the name given to all those populations living in the central and southern part of the peninsula because of their habit to worship the "vitello" (calf) or to breed calfs.
Before becoming a politically united nation, they used to speak the very same language from Sicily to Piedmont, from Veneto to Sardinia. "Italia" was a geographic expression only for the blinds.
America has been named after Amerigo (Americo) Vespucci, the Italian explorer who recognized it was actually as a brand new world. And so on.
Yes, Italy doesn't seem to be that united today. The same happens to Spain, the United Kingdom and even the USA sometimes show cracks in the union between the two coasts...
Source? According to linguist De Mauro, before the Italian unification the percentage of Italian speakers was around 2.5% (on 25 millions inhabitants). Most of the people were speaking their own dialects, which - albeit descending from Latin - are not necessarily mutually intellegible
Mine is here: https://it.wikipedia.org/wiki/Lingua_italiana#Dal_latino_vol...
I guess it very much depends on whether you consider writers, academics, and in general literate people, or the majority of the populace. In the former case, it's true that Italian was used across the peninsula.