The matter at issue here is the identification of the Hebrew word: כַּשְׂדִּי (Kasdi or Kasdimah) which is uniformly translated Chaldea. That is, כַּשְׂדִּי is identified with the ancient Chaldean empire, or ancient Babylonia. See H=GenGen 11:28, 11;31, 15:7, 2 Kings 24:2, 25:5, 5, 10, 13, 24, 25, 26, 2 Chron 36:17, Neh 9:7, Job 1:17, Isa 13:19, 13:19, 23:13, 43:14, 47:1, 5, 48:14, 20, Jer 21:4, 9, 22:25, 24:5, plus more in Jeremiah, Ezekiel Daniel, Habakkuk, etc.
Notice that whatever we might make of the ancient words, the same words were used much later by writers familiar with the then current events such as Jeremiah, Ezekiel and Daniel.
That the Chaldean empire/BabloniaBabylon/Sumer was located in Mesopotamia (= "between the rivers" of Tigris and Euphrates), has been established beyond reasonable doubt by archaeological records dating to 2000 BC.
If one wishes to correct the Bible record, then such a correction would be based far more on what is unknown than what is known. I see no difficulty identifying כַּשְׂדִּי with ancient Chaldea, or the empire of the Chaldeans.
Lastly, I have seen Chaldean records, specifically from Ur that contain the (apparently common) name "Abram". Therefore, Abram appears to be have been a name in common use in that area at the time.