Who was Darius the Mede?
It is often suggested it was Gabaru (also called Gobryas or Ugbaru). It needs to be understood that this general entered Babylon on the 16th Tashritu (Tishri) but died on the 11th Arahshamnu, which was the following month. He lived less than a month after capturing Babylon. The length of time needed for the events relating to Darius the Mede in the book of Daniel mean Gabaru must be excluded as a possible candidate. See "The Ancient Near East, an anthology of texts and pictures" Ed. James Pritchard; 2011; pages 281 -282.
It is often claimed that there is no evidence of Darius the Mede outside the Bible in the book of Daniel. Those who claim this tend to accept the testimony of Josephus, writing in the first century ad, and tend to dismiss the testimony of earlier writers.
It is obviously true that the currently available evidence is sketchy; had there been no demise of the ancient library at Alexandria in Egypt and at Persepolis in Persia (destroyed 330 bc) we would doubtless have much more extra-biblical evidence.
A hint from Berossus, writing beginning of 3rd century bc
C. F. Keil in his commentary on Daniel quoting Berossus wrote:
"Cyrus, after he had taken possession of Babylon, appointed him [Nabonidus] margrave of the country of Carmania. Darius the king removed him out of the land." (See page 1061 of https://archive.org/details/biblicalcommenta00keil9/page/n1057/mode/2up?q=Darius)
A comment is made on this in an article by Stephen Anderson and Rodger C. Young:
Nabonidus was between sixty-five and seventy years old when he became king [of Babylon] in 556 BC which means that he would have been between 99 and 104 years old when Darius Hystaspes ascended to the throne in 522 BC, if he were still alive (possible, but unlikely). In addition, the mention of King Darius is in the context of the fall of Babylon and before Berossus concluded his account of the reign of Cyrus, or even of the career of Nabonidus. Thus, Berossus seems to have believed that there was a King Darius who reigned concurrently with Cyrus and who had greater authority than Cyrus within the Medo-Persian Empire.
Evidence from Harpocration
In the same article of Anderson and Young:-
Valerius Harpocration was a lexicographer who wrote in the latter half of the second century AD and who was a tutor of the emperor Verus (reigned AD 161-169). He was associated with the great library at Alexandria and consequently had access to many ancient books that later were lost when the library was destroyed. His only surviving work is "Lexicon of the Ten Orators", a glossary to terminology used by Greek orators. The portion of Harpocration's work that is significant for the issue of Darius the Mede is his entry for the word "daric". Herodotus claimed that Darius Hystaspes invented the daric coin as a memorial to himself (Histories 4.166). By contrast, in Harpocration's entry for "daric," he wrote, "But darics are not named, as most suppose, after Darius the father of Xerxes, but after a certain other more ancient king." This is the second reference that Keil cited as evidence, outside of the book of Daniel, for the existence of Daniel's "Darius the Mede" as a historical figure.
For further reading see the online article:
"THE REMEMBRANCE OF DANIEL'S DARIUS THE MEDE IN BEROSSUS AND HARPOCRATION" by Steven D. Anderson and Rodger C. Young http://www.rcyoung.org/articles/darius.html
See also "The identifications of Darius the Mede" by Dr Steven Anderson at www.stegozoeterno.org
Dr Anderson received his doctorate studying the identification, "Daniel the Mede: a reappraisal". Or you can read his shorter article "Darius the Mede: a solution to his identity".
See also the wikipedia article on Cyaxares II which presents both sides of the argument as to whether he existed. If Cyaxares II did in fact exist then his story matches very closely the sketch of Darius the Mede we have in the book of Daniel. As for the objection that "Cyaxares" does not sound like "Darius", monarchs did, and still do, give themselves coronation/throne names which are not necessarily their birth names.