To search for the described part, use the keywords potentiometer with detents.
The specifics mentioned would suggest a potentiometer with 10 detents, such as this one on Amazon, or another on Jameco.
The detents can be low torque (a gentle click at each transition) or high torque (a firm click). The common / inexpensive ones are low-torque, but they seem to survive longer than a few high-torque pots with detents I have used.
More expensive such potentiometers allow individual mechanically adjustable detent torque, even to the extent of mixing high and low torque detents within a single pot (example).
At the high end of the spectrum, some manufacturers offer programmable detent torque: Internally these are essentially like stepper motors integrated with the potentiometer shaft, with the externally controlled coil current determining the holding torque at each detent position. I haven't seen this type available in retail, only through OEM sales by quotation.