I have some previous answers that may be helpful:

What did the other people's of Europe call the Byzantine Empire? Did it differ depending on who you asked and were there any changes as the empire dwindled?

In general we could say people in Latin western Europe stopped considering it the true empire by the late 8th century, when the empress Irene overthrew her son. In the west Charlemagne and the pope decided to "restore" the western empire by crowning Charlemagne emperor in 800.

But as for why modern historians call it "Byzantium", that is also confusing and complicated and one single answer doesn't really do it justice, but I have another answer that might help:

Why is it called the Byzantine Empire when the city was known as Constantinople for centuries longer than it was called Byzantium?