Why mechanized US Army units still use cavalry names

Why does the US Army still call units cavalry when they use motorized or mechanized vehicles instead of horses?

Cavalry is a rapid-mobility and combined-arms function; armored vehicles now perform the maneuver, seizure, and holding tasks once associated with mounted troops.

Cavalry is a battlefield function based on rapid mobility. These formations use speed to seize ground before slower forces can respond. They also need enough firepower to hold what they take, making them combined-arms units. Mechanization changes how they move while preserving the function associated with the cavalry name.