Asshur is the Hebrew word for Assyria, which produced on the greatest world empires of the past along with Babylon and Egypt. Without exception, every time the words Assyria or Assyrian appear in the Old Testament, it is translated from the word Asshur. Asshur was also the name of the major god of the Assyrians. Here’s another example of a nation that deified its long-lived ancestor.
There is no race of people who bear the name of Arphaxad. Josephus says that the Chaldeans are the descendants of Arphaxad, and he is probably right, but it does seem possible that the reason there is no race of Arphaxadites is that his name was eclipsed by the name of his grandson Eber, from which we get the word Hebrew. Until the time of Abraham, Eber was the only descendant of Shem who outlived him. Eber outlived his great-grandfather Shem by some twenty-nine years, and he probably became the patriarch of the clan rather than his grandfather Arphaxad. As a result, the name of Arphaxad is largely forgotten in the historical record, while the name Eber (Hebrew) is firmly fixed on the pages of history.