Gerard Van Groningen argues for single authorship of Isaiah.
Gerard Van Groningen, "The Messiah in the Book of Isaiah, 3: The Servant-Son," Messianic Revelation in the Old Testament volume 2 (Wipf and Stock Publishers: Eugene OR, 1997) 592-593, 614
44:28-45:13. This passage has been a major factor in the debate about the unity of the Book of Isaiah. The particular point of contention is the Hebrew name of Kores, rendered Cyrus in English. Skinner, writing as many others have, asserted that "the allusions to Cyrus in the prophecy make it perfectly certain that the time to which it refers lies between 549 and 538. ... The nation (Israel) is in exile, but on the eve of deliverance." According to nonhistorical, nonbiblical records, Cyrus was first known as king of Anshan, in Elam, a country east of Babylon. He soon become king of Persia, defeated Astyages, king of Media (ca. 549 B.C.), and thus was able to form one nation, the Medo-Persian kingdom. He then proceeded to conquer countries to the north and having succeeded, planned his attack on Babylon to the west. In 538 B.C. he captured the city and its empire and became the ruler over an area which included most of western Asia. Within two years of this victory, the exiled Israelites were permitted to return to Jerusalem. These historical facts comport with the biblical record (2 Chron. 36:22-23 par. Ezra 1:1-2).
The question to be answered is: Did Isaiah, receiving a revelation from Yahweh, prophesy specifically about Yahweh's raising up Cyrus as a delivering and restoring agent 150 years before the Persian king appeared on the scene of history? Or was there a second Isaiah who lived and prophesied at the time of Cyrus's rise to power and conquest of the nations? The answer given previously was that when Isaiah prophesied, he predicted the rise and rule of Cyrus. This answer is entirely in harmony with what Isaiah was prophesying. Consider again how Isaiah accused the covenant people of false worship (43:22), of corrupt sacrifices (43:23-24a), and of burdening Yahweh with the sins (v. 24b). These were the very sins and trespasses he had spoken of before (cf. 1:10-16). For these iniquities and evils the people were to be plundered, devastated, and destroyed (1:7-9; 3:1-26; 41:25; 43:28). This destructive judgment, however, was not to be the end of Yahweh's people (the real "burden" of Isaiah's message in chaps. 40-52); Yahweh will redeem and restore. Note also that Isaiah, living and ministering in the proximity of the temple, speaks of its restoration after it had been destroyed. How and why?
Yahweh will raise up a totally unexpected agent to deliver and restore: Cyrus! He will summon him by name and call him personally (45:14). And this foreigner will be raised up lema'an (for the sake of) two specific factors: (1) for the sake of Jacob, my servant, for the sake of Israel, my chosen one (45:4). Yahweh's election of Abraham and his seed, Yahweh's covenant with this seed, Yahweh's promises to and plans for this seed, and Yahweh's intended use of the seed to bring forth the Seed are not to be thwarted or foiled. Jacob or Israel will be helpless in bondage, brought into it by Yahweh himself. But Yahweh will break those fetters through Cyrus; thus Yahweh's people will be enabled again to fulfill their divinely intended purposes. And (2) for the sake of mankind to know that Yahweh alone is 'elohim (vv. 5-6) and that there is no other Yahweh-a faithful, covenant-keeping Lord who brings darkness and disaster but also light and life (v. 7).
Isaiah indicates in his prophecy who that person is to be; he gives his name at least 150 years before that person would appear on the scene of history. As we mentioned before, Old Testament foretelling has given critical scholars impetus to seek a second prophet named Isaiah who lived at the time Cyrus was making his debut to regal power and fame. Critical scholars have difficulty accepting the biblical teaching concerning prophetic prediction. If, however, the biblical data are consulted, one can see that frequently predictions were made by naming persons. Abraham was told about Isaac (cf. Gen. 18:10-15); Jacob named Judah as "the one" (Gen. 49:8-12); Hosea gave names to his three children which spoke of future circumstances (Hos. 1:4; 6, and 8); Isaiah gave the name of the Son to be born, names, Immanuel (Isa. 7:14) and other names (Isa. 9:6 [MT 9:5]) before conception took place. The most magnificent prediction of all by various Old Testament prophets was the coming of Jesus Christ; the New Testament repeatedly refers to his coming, presence, and work as fulfillment of predictive prophecy. In the context of this overwhelming testimony concerning precise foretelling, by which various persons were referred to by name, none need exercise or express doubt about Isaiah's reference to Yahweh's agent, namely, Cyrus.