When it's not simply referred to by its number, editors grab the first two words as its title. Why? This has partly to do with the reality of manuscript production in the middle ages: you wouldn't take up extra space on a page to place a unique title since it was expensive and time-consuming to procure the materials. (Take a look at the manuscripts in the Petrarchive to see the set-up of the pages—and the lack of titles therein.)
Using the phrase "Italia mia" in the opening line of his poem is actually historically significant. Back in 1344, Italy was not a unified nation: most Italians identified with their city or commune. Modern scholars are even squeamish when we talk about an "Italy" before the nineteenth century.
But Petrarch's use of the phrase and the sentiments in the poem itself hint at a nationalistic pride—or at least ethnic pride—despite the fragmented political nature of Italy at this time. By using the phrase and referring to all of them as "Italians," he's trying to manipulate them emotionally. But hey, it's for a good cause. He just wants the leaders of the land to simmer down.
"Italia mia" is also part of a larger work that has several names. Petrarch himself called it Rerum vulgaria fragmenta, or Fragments of Common Things. That "vulgar" bit in the Latin title isn't Petrarch being down on himself. He's just saying that the work is written in Italian, or the "vulgar tongue."
The work has also been called the Rime Sparse (Scattered Rhymes), which refers to a phrase in the first poem in the collection. And finally, the title Canzoniere (Book of Songs) has gained popularity in the last few decades. (All options are equally correct, so find the one you like and stick to it.)