Why does Isaiah not mention himself after chapter 39?

Below I have listed some key passages from a scholarly article on this subject, and I have provided the link to the much longer original article at the bottom.

"Isaiah is a remarkable book that no human alone could have written: it has knowledge of future events in his own land, as well as of the coming Messiah. For this reason, its authenticity has been attacked furiously by critics. But charges of multiple authorship make no sense of the internal evidence, the available manuscript evidence, and the testimony of Christ and the New Testament authors.

The internal evidence... Many of the same evils were denounced throughout the book, such as murder (Isaiah 1:15, 59:3,7) and hypocrisy (Isaiah 29:13, 58:2,4). Also, idolatry (Isaiah 1:29, 57:4–5) is denounced, including child sacrifice (Isaiah 57:7), although these ceased after they returned from their Babylonian Captivity.

The New Testament authors and Christ Himself clearly believed that Isaiah was a unity, which should be decisive for any professing Christian.

-Matthew 12:17–18 quotes Isaiah 42:1 as “that which was spoken by Isaiah the prophet.” ---Matthew 3:3 quotes Isaiah 40:3 as “spoken by the prophet Isaiah.”
-Luke 3:4 quotes Isaiah 40:3–5 as “in the book of the words of Isaiah the prophet.” -Romans 10:20 quotes Isaiah 65:1, stating, “Isaiah is very bold and says …” -In John 12:38–41 we find two quotations from Isaiah: Isaiah 53:1 (in v. 38) and Isaiah 6:9–10 (in v. 40). Then in v. 41 John affirms “These things Isaiah said when he saw His glory and spoke of Him.” This surely implies that the inspired apostle believed that both Isaiah 6 and Isaiah 53 were written by the same Isaiah.

There have been recent sensationalist headlines asserting that the Bible has been radically altered throughout its history. But in reality, the copying accuracy of Isaiah over a millennium has been incredibly accurate. Analysis showed that the Dead Sea Scrolls are about 1000 years older than the earliest Masoretic manuscripts, yet they are word-for-word identical for 95% of the text. Consider that wonderful chapter 53 of Isaiah, the prophecy of Jesus’ atoning death and resurrection. Of the 166 words, only 17 letters are different. Ten are spelling variants, and four more are stylistic changes. The remaining three letters spell the word ‘light’ in Is. 53:11, and may make more sense that way, although it doesn’t greatly affect the meaning of the passage. So overall, the DSS increase our already high respect for the Masoretic Text."

http://creation.com/isaiah-author-date

It is generally accepted that Isaiah chapters 1-39 were written by Isaiah, son of Amoz, who lived during the reigns of Kings Uzziah, Jotham, Ahaz and Hezekiah of Judah, although there were numerous later additions and changes to that portion of the book. Uta Ranke-Heinemann, in Putting Away Childish Things, page 230, dates chapters 24-27, the 'Little Apocalypse of Isaiah', to the late post-Exilic period. It is not unusual for an author to write about himself in the third person, and scholars accept the historicity of Isaiah and accept him as the author of the opening chapters of his book.

Chapters 40-55 are attributed to an anonymous author now known as Second Isaiah or Deutero-Isaiah, who lived during the Babylonian Exile. This author had a very different style to that of First Isaiah, who used brief, emphatic diction, compared to Second Isaiah's poetic style and more extensive vocabulary.

Chapters 56-66 are attributed to another anonymous author now known as Third Isaiah or Trito-Isaiah. The style of Third Isaiah is similar to that of Second Isaiah, but differences of content and focus create a seam in the present book.

Abraham Ibn Ezra, a Jewish scholar of Spain during the twelfth century was probably the first to raise questions about the authorship of the Book of Isaiah. It has also been proposed that the writings of II Isaiah and III Isaiah were originally separate books, but were subsequently appended to the original Book of Isaiah.