The Romans mutated their Diana to be a copy of Artemis.
Diana is often shown with a headdress made of a crescent moon.
Eventually Artemis absorbed Selene's attributes. Selene was the Greek personification of the Moon, & Luna is the Roman version.
Selene & Artemis were associated with Hecate (goddess of witches) and all 3 associated with the Moon.
English: Man in the Moon.
Japan: Rabbit in the Moon.
Insular Celts: Hare in the Moon; the Normans brought the rabbits.