Ask your average London tourist to point to St Stephen's Tower on a map and the likelihood is that they'll falter.
For that matter, ask the average Briton to do the same and there will be a few apologetic grimaces. I know this for a fact, because I did it once. With my back to the Boadicea statue and a crowd of people around me all happily snapping away at the monument looming over us.
I asked loudly if anyone knew where I could find St Stephen's Tower. Nobody could. They were all photographing it and not one person told me that. (Though the lady on the crepe stall was onto me. She winked and flicked a glance towards it.)
Yes, Big Ben is the huge bell inside the tower. The 11 storey landmark itself is St Stephen's clock tower. Shortly to become Elizabeth Tower.
Based on this precedent, I find it highly unlikely that anyone will even notice that there has been a name change; let alone stop calling it Big Ben.
Update! The comments to this article revealed precisely how British people get confused over the real name of this clock tower. The wonderful Wizzley author TerriRexson alerted me to the fact that it's not officially called St Stephen's Tower at all. That's a different tower in the Palace of Westminster.
This surprised me, so I looked it up. She was half-right. It's not officially called that at all. But neither is any other tower.
It seems that St Stephen's Hall was where Members of Parliament sat, in the original building, that was destroyed by fire in 1834. Victorian journalists would talk about 'news from St Stephen's', but not in a nice way. The term was used as a way of NOT saying the House of Commons, so it was downright derogatory to those within it.
It was a press insult which fixed the tower, in the public view, as St Stephen's Tower. It was what they used when they wanted to insult the politicians behind it. But as the memory of the Hall faded, the term lost its sting and fell out of favor. All that remains now is a folk knowledge that that is the real name of the tower enclosing Big Ben, which is precisely what I thought I knew.
The real name of the tower? *drum roll* It's Clock Tower. That's it. Clock Tower. No wonder we all call it Big Ben!