I don't know how you figure the Roman Empie lasted for two thousand years. Even saying one thousand would be stretching the facts quite a bit. The Roman Republic didn't become an 'empire' until about the time of Gaius Julius Caesar who was assasinated in 44 b.c.e. Prior to that Rome had grown from a city state, governed as a monarchy under the Tarquin kings, to an ever-expanding republic. The exact date of Rome's founding isn't known, but it's somewhere around 500 b.c.e. The Western Empire (which is all we're talking about when we refer to 'Roman Empire') came to an end in 476 c.e. with the sacking of Rome by Odoacer who promptly proclaimed himself King of Italy.
I suppose you could try to make the case that the Eastern Empire survived for about another 1,000 years until the Crusaders helped sap its strength to the point that the Muslims found it easy pickin's. But after the fall of Rome itself, that empire was known as Byzantium, or the Byzantine Empire, not Rome. It was strictly Hellenistic rather than Latinate (is that even a word?) and was hardly ever referred to as New Rome.