Hopefully they change the name, but I wouldn't count on it. Similarly, I bet the renovated arena is marketed as "Toronto" for major concerts.
Those of us from here know Hamilton is an independent place that's still far out on the "fringe" of the Toronto sphere of influence, though more and more our city is falling into orbit. Someone coming from farther away won't have a clue about this stuff, certainly not if from many parts of the US... "Hamilton? The musical? Then why is there a rock concert happening??"