Set the document title in the PDF viewer to be the name of the PDF file.

chrome/browser/resources/pdf/pdf.js

Index: chrome/browser/resources/pdf/pdf.js
diff --git a/chrome/browser/resources/pdf/pdf.js b/chrome/browser/resources/pdf/pdf.js
index 57b80c35179b1f14b2f566f7ef64464aaa848faf..ef89c325c7591e4894b81f19b084033baefbbad0 100644
--- a/chrome/browser/resources/pdf/pdf.js
+++ b/chrome/browser/resources/pdf/pdf.js
@@ -21,6 +21,16 @@ function getScrollbarWidth() {
 }
 
 /**
+ * Return the filename component of a URL.
+ * @param {string} url The URL to get the filename from.
+ * @return {string} The filename component.
+ */
+function getFilenameFromURL(url) {
+  var components = url.split(/\/|\\/);
+  return components[components.length - 1];
+}
+
+/**
  * The minimum number of pixels to offset the toolbar by from the bottom and
  * right side of the screen.
  */
@@ -81,6 +91,7 @@ function PDFViewer(streamDetails) {
                           false);
   this.sendScriptingMessage_({type: 'readyToReceive'});
 
+  document.title = getFilenameFromURL(this.streamDetails.originalUrl);
   this.plugin_.setAttribute('src', this.streamDetails.originalUrl);
   this.plugin_.setAttribute('stream-url', this.streamDetails.streamUrl);
   var headers = '';