What is the name for a reaction with a solid product rising from its container?
In pyrotechnic chemistry, they might call it a pharoh's snake (or serpent) reaction. To a degree, (or rather 330 °C) pyrolysis of the sugar is occurring (starting at 170 °C). 

In cooking, they would call it caramelization, although the term is also applicable in general chemistry. Less specifically, you can call it a "browning reaction"... note- caramelization (non-enzymatic) should not be confused with a Maillard reaction (enzymatic). More specifically, you could call it dehydration or decomposition of sugar with sulfuric acid. Somewhere in-between you might find the term carbonization.

You may also find the terms carbon soufflé and carbon foam interesting.