What the names ''Big Ben'' ( for example ) are refering to remains a bit unclear to me because of these discussion above, but I would like to say that changing the name ''Big Ben'' to ''Elizabeth Tower'' seems both extremely unnecessary to me and would probably cause national or even international disappointment.
Basically, people reffer to the whole tower as being "Big Ben" - it's just what we do, however, this is actually incorrect, it's formal name is "The Clock Tower". The face that you see in most pictures (
This One) is called the Great Westminster Clock. (More commonly - the Great Clock)
The biggest bell inside of it is Big Ben.
So actually, Big Ben isn't being renamed - just the name of the tower is.