What do we call the process of movement of nutrients across the surface cells of the villi into the blood?
I would say either absorption or assimilation.
Absorption is the process of movement of nutrient molecules across the villi of the small intestine into the blood. Then, they are made into parts of cells and tissues in the body, and that process is called assimilation. Absorption rate is highly increased by thin surface walls and large surface area, which the small intestine is highly adapted to.