Egyptian
Thoth
writing, moon, wisdom
Japanese (Shinto) tradition. See the whole pantheon.

Born from Izanagi's right eye. In the Nihon Shoki he kills the food goddess Ukemochi in disgust, after which Amaterasu will no longer face him, which is why sun and moon are apart.
All sources for the Japanese (Shinto) pantheon
Lineage in the sources used: Izanagi.
Deities in other traditions who share a theme with Tsukuyomi: the moon. This is overlap in one area only.
Egyptian
writing, moon, wisdom
Mesopotamian
moon, wisdom of time
Aztec (Mexica)
the moon (by interpretation)
Chinese
the moon
Roman
the hunt, the moon, childbirth