Have you heard of the Nestorian Christians in the mountains that might be known as Assyria?
Sure, even Marco Polo encountered colonies of them, IIRC.
They survived as well in Central Asia for centuries.
As far as Assyria, the name of the country as such was pretty much absorbed into the Persian Empire, and seems rather nebulous after that period.
Guess I don’t quite understand your question “might be known as Assyria”?