Why is force called the rate of change of momentum? Why is force called the rate of change of momentum?
If I push a wall I do exert a force but there is no movement; so is there force acting on the wall?
 A: According to Newtonian mechanics, the state of rest or uniform motion is changed due to applied forces. for instance let me consider i am standing at a place for more than hour, my foot becomes painful though i never applied any force on the floor or floor is exerting some force on me. 
If you apply some force on a particle, then the work done by the force will result in change of motion causing a displacement along the same direction of applied forces. Now coming to your question let me assume that you keep on exerting the force on the wall for prolong time, but this results nothing so, ultimately there is no work done. finally you became tired by applying force on the wall. 
If the applied force is more in magnitude comparing to the object than only it results in motion or displacement, work done on a particle will explain the change in force along the direction of displacement. 
A: 
Why is force change in momentum?

It isn't. The proper sentence would be "Why is the sum of forces rate of change in momentum?".
We don't write $\vec F=d\vec p/dt$, we write:
$$\sum\vec F=\frac{d\vec p}{dt}$$
(Note, as another answer says, we are not talking about simply change of momentum $dp$ but rather rate of change of momentum $dp/dt$, and I assume that that's what you mean.)
This is Newton's 2nd law. Notice the summation sign $\sum$. One force doesn't imply momentum change necessarily. Your wall example is a good example. Or simply a book lying on a table. Force is exerted to hold up the book, but no momentum change happens.
If there is a net force - that is, if the sum of forces is not zero - then you do have a momentum change according to Newton's 2nd law.
A: Force is defined as the rate of change of momentum, not change of momentum:
$F=\frac{dp}{dt}$
An impulse, $J$, defined as the integral of the product of force and the time during which it acts, however, causes a change in momentum:
$J=\int Ft\;dt =\Delta p$
Interestingly, in Isaac Newton's Principia Mathematica, Newton originally stated the Second Law of Motion in the impulse format, not in terms of an instantaneous force.
When you push on a wall, you exert a force on it, but you don't notice the effect due to its support; other forces are acting on it which cancels your force. Remember, the effect of exerting multiple forces on a single object depends on the vector sum of the forces, not due to a single force.
