Is there an HTML editor that automatically changes the end tag when editing the start tag?
Aptana Studio Does. Just set the pair change tag in the menu "Window"> "Settings"> "Aptana"> "Editor"> "HTML"> "Enter". By default it is disabled.
IntelliJ has a bunch of XML refactors , one of which is a rename tag.
e-texteditor can do this, although not as automatically as you probably want. Ctrl + doubleclick at the beginning and end of the tags and change them that way.
IntelliJ IDEA 14.1 has this feature:
http://blog.jetbrains.com/idea/files/2015/02/simultaneous_tag_editing_2.gif
For example, if you want to change divto spanin:
div
span
<div> Text </div>
enough to edit one of the tags and the other will be changed in real time.