Compared to the earlier 5th century, many things indeed remained the same.

To quote Goldsworthy's "Fall of the West":

As far as possible, [Odoacer] preserved the existing regional and administrative structures. The Senate still met and there continued to be city prefects and other magistrates at Rome. Major repairs were conducted on the Colosseum in 484. The absence of an emperor in the west may not have been immediately obvious to many living in Italy, let alone the other provinces. Imperial power had long since become so weak as to make the western emperors almost irrelevant. With hindsight, many in the Eastern Empire saw the year 476 as significant.

And later, on Justinian's reconquests:

Ironically, the fall of the Ostrogothic Kingdom [in Italy] in a long and costly conflict, followed not long after by the Lombard invasion, probably destroyed many aspects of Roman culture and society that had survived the collapse of the Western Empire.

Or Peter Heather, in his "Fall of the Roman Empire":

During the same period there were many living in western Europe and North Africa who continued to think of themselves, and were thought of by others, as Romans. [...] Over time, the distinctions were eroded, but it took several generations.

Heather holds that in many places, including parts of Italy, "Local Romanness" survived.

Roman landowners had much to offer the new barbarian rulers, and, as a result, their regimes were willing broadly to uphold the unequal distribution of property that had brought the landowners into existence in the first place. We see remarkably little in terms of social upheaval, then, south of the Loire. [...] In Spain and Italy too, the Roman landowning class generally survived the first shock of the end of Empire.

Heather holds that "Romanness" ended with the Arab invasions in the 7th century. Other historians too have in recent decades argued for even more continuity:

"It should be clear [...] that the Roman Empire did not "fall" in the fifth century, but was transformed into something new." - P. Barnwell, Emperors, Prefects and Kings: The Roman West, 395-565 (1992) p. 174

This is probably pushing the balance a bit too far in the other direction. Life in the Germanic successor-states in the West was not the same as it had been under the emperors, and the differences grew more pronounced over time. But perhaps someone better read in social and economic histories of the period can offer more detail on that.