The proper name given by the Pope to describe the ethnic Assyrians who split from the Assyrian Church Of the East to the Roman Catholic Church known as the Great Schism. They speak a dialect of Chaldean Neo-Aramaic. For four centuries the Catholic Church tried to convert the Assyrians to Catholicism. It must be mentioned that the Assyrians of different religious denominations (Orthodoxy, Nestorian, Catholic, Maronite etc.), due to their lack of education, are not united as one nation but hate each other, thinking the others are foreigners!
The King of Assyria; Essarhadon, had 2 sons named Ashurbanipal (who had already been in control of Nineveh to the North) and Shamash-shum-ukin (The Predecessor of KALDU). After King Essarhadon's death, Babylonia was left to be governed by his son Shamash-shum-ukin and eventually revolted against his brother in 652 BC. In 626 Bc, Babylon had eventually threw off the Assyrian rule under King Nabopolassar's reign thus creating the Neo-Babylonian Empire (Chaldean Empire) with Babylon as the capital.
Ahura Mazda, God of Zoroastrianism founded as one of the Oldest religions that still exist today was actually founded by King Darius who was not a legitimate King of the Persian Empire after he plotted to kill the real King, Bardiya (son of Cyrus the Great founder of the Persian Achaemenid empire) until he had introduced Ahura Mazda and that he was chosen by him to be King so that the people within the empire would not Rebel against him. It is also a fact that Ahura Mazda actually had been a off-shoot of the Ancient Assyrian
(Which is also where the name came from) who were a part of the Persian Empire.
Modern day Parsees of India follow Ahura Mazda