Talking from a medievalist's point of view, the general concept of Italy has seen some varying diffusion over the centuries. While back in Roman times - both Republican and Imperial ones - the peninsula as a whole was effectively reffered to as Italia, much like it is called in modern Italian, already during the closing decades of the Western Roman Empire, "regionalization" of the political entities of continental Italy was taking place alongside other divisions based on ethnic principles.

To clarify my statement, the Langobard migration of 568 which settled most of Italy, likely upon request of the Byzantine emperor, already provides some hints regarding the partial eclipse of the geographical concept of Italy. The places settled by these Germanic peoples stretch the length of the peninsula, except port cities like Genoa, Naples, Ravenna and others which were defended by Roman fortifications and navies (two things the Langobards never managed to overcome), the two islands of Sardinia and Sicily, the southern regions of Puglia and Calabria (for most of the Early Middle Ages at least, due to Byzantine presence) and Rome, still strong enough to dissuade invaders.

For virtually five centuries - up until the Norman conquest of the south of Italy in the XI-XII centuries - Langobard presence in the shape of both a kingdom based in Pavia and several regional duchies spread across the peninsula, the whole of Italy was partially renamed due to this massive political-ethnic shift. Southern duchies were at times called Langobardia minor, while center and northern ones were referred to as Langobardia maior. The territories still held by the Exarchate of Ravenna were called Romania, "the place of the Romans" (Romans meaning Eastern Romans, the Byzantines), morphed in the modern-day Italian region of Romagna. Italy was virtually renamed "land of the Langobards", or Langobardia which named the currrent region of Lombardia.

After the fall of the Lombard king Desiderius in 774 after Charlemagne's conquest, his title was "king of the Franks and the Langobards", Rex Francorum et Langobardorum. After his death, the epilogue of civil wars between his sons and nephews, in the second half of the IX century, several kings of Italy appear on the scene already with Bernard (d. 818) nephew of Ludwig the Pious (778-840) and then with Ludwig II (822/5-875). However, the Italy they ruled over was most likely the upper half of the Peninsula, excluding much of the territory held by the Lombard dukes who effectively ruled as independent in places like Spoleto, Benevento and Salerno.

In a sense, the geographical concept of Italy seems to have been partly obscured by its political concept, now apparently limited to the portion once ruled by Carolingian sovereigns and now part of the Holy Roman Empire and thus under the influence and government of German emperors.

It is likely, however, that after the XI century a broader idea of Italy as a contiguos area of similar cultures starts to constitute itself. Some scholars believe it is linked to both a linguistic and cultural resurgence connected with both the renewed studies of Roman Law and the formation of the first universities, like Bologna in 1088, and the creation of the potentially first iterations of poetry and literature in vernacular speech (the Sicilian school of poetry, active in the 1200s, may had had its beginnings some decades earlier). This also meant the gradual decay of the ethnic differences in place during the V-IX centuries, especially linked to judicial matters (the Edictum Rothari of 643, the first ever codification of Langobard oral laws explicitely marked the difference of legal systems to be applied to a case if there were Lombards or Romans involved).

All these elements could have influenced the various interpretations given to the idea of Italy during its history (at least, in the Middle Ages).

I hope this overview helps your inquiry.