Beth Nahrin is the geographical name and Assyria is the political name for our homeland.
And we call our ethnicity/people/nation as Assyrian by sayin Suroye/Suryoye because this means translated Assyrian.
But most are not aware about this fact, because they have no education + noch healthy mentality (all because of the persecution during centuries, and its traces are so deep that it reachs our generation + a few more).
Most think that Suroyo means Christian although mshiHoyo means Christian ... but even in our daily speech we can see that Suroyo means not Christian, e.g. if we visit somebody on Christmas or Easter and than go away, we say: "aloho soyem d ´aidhitun u ´edhathkhun b kol shato b sheyno u Hubo"
... and the answer is traditionally: "kol Suroyo mshiHoyo"
So does that mean "every Christian is a Christian" ??? No!
And Suroyo/Suryoyo does not come from Ossuroyo, it comes from Ashuru ... see here:

2 weeks ago we had a seminar with Prof. Dr. Robert Rollinger in our Assyrian culture club, he´s the man who found the stone tables which confirm that Suroyo means Assyrian, and he spoke about that, too. And he told that already the Assyrians in the Assyrian Empire called Assyria Syria (especially the western part), and everybody knew Syria is Assyria.
So if we speak in our language, we all call ourselves and our language Assyrian by saying Suroyo/Suryoyo and Surayt.