An example of this is the Chaldean origin of the Neo-Babylonian Empire. It is generally assumed that the Nebuchadnezzar, who sacked Jerusalem and took the Jews captive into Babylon, was part of a dynasty that was Chaldean in origin. Thus the Jews were captive in Babylon, in Chaldea, and the Chaldeans were another name for the Babylonians. That may not be the case though. As Paul-Alain Beaulieu points out in a recent article:
Not only do we find no ancient claim for the Chaldean origin of the dynasty, but the term Chaldean does not appear even once in late Babylonian cuneiform documentation. (Paul-Alain Beaulieu, "Arameans, Chaldeans, and Arabs in Cuneiform Sources," in Arameans, Chaldeans, and Arabs in Babylonia and Palestine in the First Millennium B.C., ed. Angelika Berlejung and Michael P. Streck [Wiesbaden: Harrassowitz, 2013], 33.)Beaulieu points out that there are over 60,000 late Babylonian sources (ibid., 31). The Chaldeans did exist; they appear in Neo-Assyrian sources. Apparently, in Neo-Babylonian times, though, they no longer thought of themselves as Chaldeans. Another alternative is that Chaldeans may have always been an outsider designation (by Assyrians, Jews, Greeks, Romans).
This has some implications for those who would argue that Abraham's Ur of the Chaldees was located in southern Babylon based on the fact that the Neo-Babylonians thought of themselves as Chaldeans. As far as we know, they didn't.