what are other names for a pottery wheel
there aren't really other words for it. Maybe kick wheel, which would refer how you get the wheel to turn. Or you could just say wheel if everybody around you knows that you are talking about pottery wheels. There are different kinds of wheels used in pottery, e.g. a banding wheel. But you wouldn't throw a pot on a banding wheel, you might handbuild one.
Other than a pottery wheel, the most used term would be the potter's wheel. It has also been called a potter's lathe. Other types of wheels include: --kick wheel --treadle wheel --electric pottery wheel, or motor driven wheel In ancient times, potters made turntables, or tournettes, to use to coil pottery faster which they turned by hand. Later the coiling turned into throwing the pots as the wheel progressed. Sometimes this was done with a stick put in an indentation in a round stone that the potter turned. In some third world countries it is still done that way. When the kick wheel was invented, it made the work much easier. The treadle wheel, like the one Bernard Leach used, also was a precursor to our modern electric pottery wheel.