What is the name for a thunderstorm with a deep, rotating updraft?

A thunderstorm with a deep, persistently rotating updraft is called a supercell. Its defining rotating circulation is known as a mesocyclone.

Supercells develop when a powerful updraft interacts with strong vertical wind shear, meaning wind speed or direction changes with height. The updraft tilts horizontal rotation in the atmosphere into a vertical circulation, allowing the storm to remain organized for much longer than an ordinary single-cell thunderstorm. Supercells are often isolated and can dominate local weather for hours.

They are the least common of the four main thunderstorm classifications, alongside single-cell storms, multicell storms, and squall lines, but they can be especially dangerous. Possible hazards include giant hail, destructive straight-line winds, torrential rain, flash flooding, and tornadoes. A supercell does not automatically produce a tornado; only a minority do. Microbursts are localized powerful downdrafts, while squall lines are organized lines of thunderstorms rather than one rotating storm.