The word “daisy” comes from the Old English dægesege, formerly dæges eage, meaning “day’s eye,” because the petals of some species of daisy open at dawn and close at dusk.
For the same reason, in Medieval Latin, a common term for daisy was solis oculus, meaning “sun’s eye.”
The name Daisy was at one time a pet form of the name Margaret because Marguerite, the French version of the name, is also a French name for the oxeye daisy.
Here’s a time-lapse of an English daisy opening in the sun:
… and here’s one of more dramatic African daisies.