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

chrome/browser/resources/pdf/pdf.js

 // Copyright 2013 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 'use strict';
 
 /**
  * @return {number} Width of a scrollbar in pixels
  */
 function getScrollbarWidth() {
   var div = document.createElement('div');
   div.style.visibility = 'hidden';
   div.style.overflow = 'scroll';
   div.style.width = '50px';
   div.style.height = '50px';
   div.style.position = 'absolute';
   document.body.appendChild(div);
   var result = div.offsetWidth - div.clientWidth;
   div.parentNode.removeChild(div);
   return result;
 }
 
 /**
+ * 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.
  */
 PDFViewer.MIN_TOOLBAR_OFFSET = 15;
 
 /**
  * Creates a new PDFViewer. There should only be one of these objects per
  * document.
  * @param {Object} streamDetails The stream object which points to the data
  *     contained in the PDF.
@@ skipping 40 matching lines @@
   this.plugin_.addEventListener('message', this.handlePluginMessage_.bind(this),
                                 false);
 
   // Handle scripting messages from outside the extension that wish to interact
   // with it. We also send a message indicating that extension has loaded and
   // is ready to receive messages.
   window.addEventListener('message', this.handleScriptingMessage_.bind(this),
                           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 = '';
   for (var header in this.streamDetails.responseHeaders) {
     headers += header + ': ' +
         this.streamDetails.responseHeaders[header] + '\n';
   }
   this.plugin_.setAttribute('headers', headers);
 
   if (!this.streamDetails.embedded)
@@ skipping 497 matching lines @@
               this.streamDetails.tabId != -1);
   },
 
   /**
    * @type {Viewport} the viewport of the PDF viewer.
    */
   get viewport() {
     return this.viewport_;
   }
 };