Looks like we don't have to wait till the story patch after 5.4 to see who our new Warchief will be:
http://www.buffed.de/World-of-Warcra...ckton-1084635/buffed: We will also have the initiation of the next warchief. How is this going to proceed?
Chilton: In patch 5.4 there is a cinematic after Garroshs' defeat in which the new warchief will be selected. So players can experience that soon.
(video interview is in english, written article in german)