Where did the name of animals come from?

Mammals are called are called mammals because they have mammary glands( also called breasts, teats or udders), which allow mammals to nurse their babies.

And yes all mammals must have the presence of hair follicles to be considered mammals.

2nd Answer:

Mammals are animals that give live birth and have mammary glands to nurse their young.

Mammals get their name from the mammary gland found in all mammals, which produces milk for their young.