The material derivative computes the time rate of change of any quantity such as temperature or velocity for a portion of material moving with a velocity. If the material is fluid then the movement is simply the flow field.
The three other names of material derivative
1. Eulerian derivative
Eulerian derivative is used when the if the material derivative is used to transform from the Lagrangian reference frame to the Eulerian reference frame
Total derivative is the derivative with respect to the function that depends on the variable not only directly but also via the intermediate variable.
The derivative of a function of two or more variable with respect to one variable the other will be treated as constant.