Plants grown upon the other plants without absorbing food from them are called

Plants that grow up on other plants without absorbing food from them are called Epiphytes.
Epiphyte, also called air plant, is any plant that grows upon another plant or object merely for physical support.
Epiphytes have no attachment to the ground or other obvious nutrient sources and are not parasitic on the supporting plants. It derives its moisture and nutrients from the air, rain, water (in marine environments), or debris accumulating around it.