Ok, you're a little wrong here when talking about the Romans, and I can point you towards sources that prove it.

The Romans used multiple names over the course of them being aware of the islands. Initially it appears they considered them all under one banner 'Insulae Britannia'. Pliny the Elder for example in his Natural History states:

'It was itself named Albion, while all the islands about which we shall soon briefly speak were called the Britanniae.'

Initially it seems that the original Latin name for Great Britain was actually Albion with Britannia referring to the whole archipelago. This is how the Greeks viewed the islands as well (Pytheas and Pseudo-Aristotle for example).

Later this collective term appears to have been dropped. This separation may well have been due to the Romans only occupying part of one of the islands as you stated. It may even be simply that because their borders were closer and they had a better knowledge of the area, so they required a more precise naming system.

If you are looking for an argument as to why these sources shouldn't mean the islands should be called ' The British Isles' today, It would probably make more sense to note that some of the sources which consider both islands as part of 'Britannia' also include the semi-mythic land of Thule as part of the set of islands (which might have been Iceland, but also might have been purely made up).