We call this style of pizza ‘deep dish’ here in Detroit which, I suppose, is just another name for the baking tray its cooked in. Though as the other commenter said, the deep dish allows you to cover it with cheese right up to the edge, which usually ends up dark and crunchy where it touches the pan.

I’ve known people to fight over the corner pieces and I think it was Jet’s that has a whole thing with an “8-corner pizza” (as in, two smaller pizzas in a box-shaped trenchcoat, cut into quarters so that every piece is a corner piece)