The rate at which work is done is called

The answer is power.

Power is the rate of using energy or the rate of doing work. Basically, any units of energy (or work) and time can be used to generate a unit of power and can be computed as Work/time. Watt is the standard metric unit of power.
We can use a case scenario to illustrate what Power is. If you take a book and lift it a meter high, you will end up doing the same amount of work regardless of whether you lift the book slowly or quickly. However, you can increase your power which is the rate of doing work when you lift the book quickly.