well the bell will Big Ben as it always has been.

I totally get this. The misconception of the tower being called Big Ben will not change just by officially renaming the tower anything.
That's just the way it is.

Mark

Exactly, so call it Elizabeth Tower, be happy it's a cheap option, and let's all move on.
What's the big fuss?

Indeed. If it makes someone happy, who else really cares?

As many have said, most people will still know it as Big Ben whatever it may actually be called. It's been called many things in the past, but no one really cares. Awesome bell is awesome, but the tower will never be anything more than chez Big Ben.