I'm reading The Ecclesiastical History of the English People (Bede, i.23, Colgrave and Mynors) and Bede says:
"In the year of our Lord 582, Maurice, the fifty-fourth from Augustus, became emperor; he ruled for 21 years."
Does this mean Bede still viewed the Empire as existing at this time but in a smaller form?
A Roman emperor being crowned in 582 shouldn't be any surprise given the Roman empire persisted for nearly another 900 years after that point! The EASTERN Roman Empire was still the Roman empire. That's how they saw themselves, and that's how others saw them (for a while at least, as you'll see in the linked answer). When people talk about the fall of the Roman Empire in the 5th century (a whole other big discussion topic) they mean the Western empire. The eastern portion with its capital in Constantinople (now Istanbul, not Constantinople...) was going strong.
If you're not familiar with the long persistence of the eastern Roman empire that's probably because history now usually calls it the Byzantine empire (after Constantinople's old name of Byzantium.
u/WelfOntheShelf talks a bit about the naming conventions here: https://www.reddit.com/r/AskHistorians/comments/ddgwg9/what_did_the_other_peoples_of_europe_call_the/
https://www.reddit.com/r/AskHistorians/comments/sy2hfw/why_do_historians_insist_that_the_byzantine/