That Endymion is called both a Shepherd and a King for awhile had me thinking David is the only other "mythological" figure he could viably be compared to. And while that connection is still one I'm perusing. I eventually remembered that on the Sumerian Kings List the Antedeluvian Dumuzi/Dumuzid (from which the name Tammuz comes) was called a Shepherd.
En is a Sumerian honorary prefix usually translated "lord". Also an -on often winds up added at the end of Greek transliterations of foreign names (this Greek feature is the only reason we call Babylon that, in the Hebrew/Aramaic text of the Old Testament it's always Babel/BBL, it's also traditionally viewed as why we spell Solomon that way). For those two reasons, I could see Lord Dumuzi being corrupted to Endymion in Greek. Also Damu is another form the name of Dumuzi used in a text titled In the Desert by the Early Grass.
The genealogy of Inanna/Ishtar is contradictory in various Sumerian/Akkadian and other Mesopotamian sources. Sometimes she's the daughter of Anu directly, sometimes of Enlil. But in one of the oldest Sumerian poems about her relationship with Dumuzid called Inana and Bilulu: an Ulila to Inana she is specifically depicted as the daughter of Nanna aka Suen/Sin (The Moon god) and his wife Ningal. Which gives a pretty strong basis for seeing her as a Lunar Goddess.
So basically, Inanna=Selene and Dumuzid/Tammuz=Endymion.
This is not the only Greek version of this Sumerian myth, as it's usually more commonly compared to Adonis, the Adonia happens the same time of year the Women wept for Tammuz. But remember Greece also had multiple Flood legends. In the Adonis tradition Inanna is Aphrodite, so that's the version that came through Cyrpus. I also believe Eos and other Indo-European Dawn Goddess (plus Uzume in Japan) are also an aspect of Inanna/Ishtar.
What's interesting is how I could stretch this analogy beyond just the original Greek Myth and make it match even more by comparing it to the Lore of the Manga/Anime franchise Sailor Moon, starting with Ningal as Queen Serenity.
Bilulu could be compared to either Beryl or Queen Metaria. Metaria could also perhaps be compared to Ereshkigal, though that basically becomes a female version of the turning Hades into Satan trope.
The loyal Maid-Servants of Inanna like Ninshubur could perhaps be the other Sailor Senshi in this analogy, and I'm oddly attracted to Makoto as Geshtinanna. It's also theorized that Inanna and Ishtar were originally separate deities later merged together with Ishtar being originally mainly a name for the Planet Venus, so that makes Ishtar as Sailor Venus an interesting option since Sailor Venus was sometimes a body double for the Princess.
The four Shitennou could perhaps be compared to people like Lulal and Shara who were governing other cities under the sway of Uruk. Also Ningishzida who was a brother in-law of Dumuzi and sometimes paired with him.
I simply lack a Sailor Moon character to compare Girgire/Jirgire to, besides that maybe in a different way he also plays the role of the Shitennou.