THIS MIGHT SURPRISE YOU
The answer
Disagree. The prophet is named in the first half: in three headings (Isaiah 1:1, Isaiah 2:1, Isaiah 13:1) and three stories (Isaiah 7:3, Isaiah 20:2 and chapters 36 to 39). After chapter 39 his name never appears again. Chapters 40 to 66 come from a voice with no name.
Why it’s interesting
The first half calls the Lord "the Holy One of Israel," and so does the second. The phrase occurs over thirty times in Isaiah and rarely elsewhere. Scholars point to links like that as a reason the parts read as one book.
Scholarly consensus
Learn the Bible.
Not just the stories, but the history, authorship, and scholarship behind it.