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I know we have mono potentiometers and stereo potentiometers, when there are two potentiometers connected mechanically. What do you call a potentiometer consisting of four mechanically connected potentiometers? Do we have a name for it?

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A ganged potentiometer is two or more variable resistors of the same or sometimes different value, ganged together on one adjusting shaft, normally used on stereo systems as a volume control so that one can vary the volume of both channels at the same time.

Ganged Pot

They are commercially available with from two to four sections.

Ganged pots are also used for tone controls, pan controls, as well as in power supplies and other electronic lab equipment.

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    \$\begingroup\$ Pots are also available with a hole in them through which a shaft may be placed [they expect the shaft to have either a notch or a flat side]. Depending upon the length of the shaft, one may be able to stack an arbitrary number of such pots on a single shaft, with any desired mix of values. Sometimes one may use one pot with a built-in shaft and stack other pots on it; other times one may have a shaft which is attached to some other assembly, so none of the pots actually has a shaft. \$\endgroup\$ – supercat Feb 19 '13 at 16:53
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Aside from Ganged, other common names are Quad Potentiometer, or 4 Channel Potentiometer.

Although multi-channel pots are more common in digital IC versions, due to size saving packages they come in, and are easier to construct.

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    \$\begingroup\$ Digital pots generally require that the voltage on every connection stays within the power rails. Multi-channel mechanical pots have the advantage that provided adequate clearances are maintained (and in some cases, insulating connectors are used), one may have hundreds or even thousands of volts between connections. This can be useful if a low-voltage pot is used to sense the position of a pot which operates a mains-powered motor controller. \$\endgroup\$ – supercat Feb 19 '13 at 16:56

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