>>Go to Properties window and change Name property
>
>When I highlight WebForm1 in Object Browser, the Property window does not react.

OK, I see the difference. My project was C#, yours in VB.
Then double-click on WinForm1 class in Class browser, go to the code window and change it there:

Public Class WebFormMichel
    Inherits System.Web.UI.Page

However, I would expect the .Net IDE behave consistently... :)