Egyptian
Thoth
writing, moon, wisdom
Roman tradition. See the whole pantheon.

Worshipped in a grove at Nemi near Rome, where the priest, 'king of the wood', had to kill his predecessor.
Greek counterpart: Artemis on thegreekgods.org. Roman and Greek versions share names and stories in many places but began as different cults.
Deities in other traditions who share a theme with Diana: the moon. This is overlap in one area only.
Egyptian
writing, moon, wisdom
Mesopotamian
moon, wisdom of time
Japanese (Shinto)
the moon, night
Aztec (Mexica)
the moon (by interpretation)
Chinese
the moon