I know that granulocytes consists of neutrophils, eosinophils, and basophils but why is this group called granulocytes? What does each type of granulocyte do?
They're called that because they look like they have little granules in them. Anatomists and histologists often start out with describing what they see, and they often see things well before any function is understood; often the names stick.
Wikipedia has a page on granulocytes: https://en.m.wikipedia.org/wiki/Granulocyte
It seems you've already gathered that they are white blood cells.