It would be a mistaken to suppose that any of the various divisions of the Empire were in effect declarations of independence, or creations of separate national entities.

In effect, these were considered administrative divisions of an indivisible whole - no different than when Antony, Octavian, and Lepidus divided the nascent empire between them three hundred years before Diocletian.

So someone living in the Gaul wouldn't necessarily consider himself a 'West Roman' different from an 'East Roman'. At least, any differences they felt did not automatically become more pronounced. It is true that as time went on and Imperial power declined, people began to feel an increasingly localized identity as opposed to an Imperial identity - but whether this was always there and just came to the forefront, or if it recurred as a result of ineffective Imperial government I cannot say. However, it wasn't a direct result of any administrative division of the Empire.

Right up until the end of what we call the Western Roman Empire, the Romans considered themselves part of one collective entity.