If you hold a glass of water in your hand, what is the name of the force acting on it, and why doesn't the force acting on it bring a change in its state of motion?

There are 2 forces acting: Gravity and the resistive force applied on the glass by your hand.

There is no change in its state of motion because they are in equilibrium, as long as you don't move your hand.

newtons first law states that an object will either remain at rest or move at constant velocity unless acted upon by a force.