This is a picture of her from the RPG.
Now, the RPG sources are not canon, but bear with me for a moment.
We know her son is Cenarius - a half Stag, half Night elf Hybrid. Now, the Stag part of him comes from Malorne (the father), so the Night elf part of him must come from Elune (the mother). So, this pretty much grounds her appearance as a Night elf.
For discussion sake, a Stag and a Naaru doesn't create a half Stag half Night elf hybrid. Neither does a Stag and a Voidlord or a Stag and a Titan.
Now, i know what you're probably gonna say: "But hey, what about the Centaur? They were produced by combining a Keeper of the Grove (Zaetar) and an Earth Elemental (Princess Theradras). According to that logic, they should have looked like a rocky Dryad or something". Well, you're right. That is the most expected outcome. The only explanation i can give is 1: Either they were affected by the Curse of Flesh (like the Earthen and the Tol'vir) or 2: Elemental traits are not passed-on through genes. One thing i can say for sure, they did get her ugliness .
People say Elune might be a Naaru, or a Lightlord (or that she created the Naaru). It was first proposed by Velen, who once visited Tyrande and told her of the similarities between Elune and the naaru. It's amplified by the fact that the Tears of Elune relic was able to unlock Xera's core and the discovery, made by Khadgar, that Elune may have created Xe'ra. The problem i have with this theory is that 1: The Light and the Naaru were formed eons before the moon of Azeroth did, and 2: Technically speaking, the moon doesn't produce light. It reflects it from the sun.
Another theory of Elune's identity is of Titan origin. The fact that Lunar spells inflict Arcane damage, the Tears of Elune being a Titan relic, or that Elunaria is home to the spirit of Eonar the Life-Binder, may suggest its plausibility. The issue i have with this theory, is that we haven't seen a Night elf-looking Titan, only Human-looking ones. We know some planets give birth to Titanic beings. The question is: would an astronomical body, like the moon (which is not considered a planet), do the same?
As for the theory of Elune being a Voidlord, i find it hard to believe as Elune is associated with feelings of tranquility and peace, rather than insanity and paranoia. Elune is said to be a source of light (even, though, not a natural one). Void magic might have star-light in its animation, but it's not actually associated with light. The duality of the moon (dark and light sides) have more in common with the Naaru, for example, going from light to dark (and vice-versa).
Let's get back to the theory of Elune being a Wild God/Loa. The Zandalari have a group of druids called Lun'alai. It is suggested that they worship Elune. Now, we know that from the Zandalari branched off several different tribes, like the Gurubashi and the Amani. It may very well be, that the Dark Trolls who branched off from the Zandalari, took the Elune worshipping with them to the Well of Eternity, and eventually became Night elves.
According to some new lore, Bwonsamdi was a priest of Mueh'zala before he was elevated to a state of Loa. Even Mueh'zala himself was probably a Troll elevated to a state of Loa by the Winter Queen, in old times. So, that means that Elune's appearance as a Night elf could be explained by the theory that Elune was once a Priestess of the moon, elevated to a state of Loa by the Winter Queen. If you look at the RPG picture of her, she does look like a Priestess of the Moon. in fact, she somewhat resembles Tyrande (especially her garment), whom is the most well-known imagery of a Priestess of the Moon.
Now, i know what you're probably thinking to yourselves: "How could the Trolls be worshipping Elune, if she only became a Loa when the Night Elves were formed?" Well... Death existed way before Mueh'zala and Bwonsamdi became Loas, so it is plausible that moon worshipping existed, but that the concept of Elune only came with the Night elves.
Why do i think Elune is a Loa, exactly? Because of the similarities of how they work. We know Loas are prayed to and bestow their powers unto their believers. The Zandalari racial depicts it the best: You pray to a Loa and gain their power. The way the Night warrior ritual, taken by Tyrande, resembles the powers granted to Rastakhan by Bwonsamdi, leads me to believe they are the same kind:
https://m.youtube.com/watch?v=V1mjyUxcjlI (the Night Warrior ritual)
https://m.youtube.com/watch?v=yNigmPEG5qk (Rastakhan vs Zul cinematic)
In both of these cases, they are pleading their "god" to grant them their power. Tyrande even makes an offering (an Orc head) to Elune at a moonwell - just like how the racial "Embrace of the Loa" has your character make an offering to a Loa at their shrine.
The only thing i can't completely comprehend is how exactly Elune is the patron god of beings from other worlds, as we learn about in Ardenweald.
It's either Elune is, exclusively, Azeroth's moon or, either, she is a universal moon goddess of all Planetary moons out there. We learn in the Shadowlands expansion that the Shadowlands is the Death realm of all living beings out there in the cosmos - not just Azeroth's. So, it is possible that through the Shadowlands, Elune became the patron god of other worlds. It is also implied that while Goldrinn is an Azerothian Wild God, he made contact with the Orcs on Draenor. If that is indeed the case, then why do we need 3 Eagle Loas (Akil'darah, Akil'zon and Ohn'ahra), 3 Death Loas (Bwonsamdi, Mueh'zala and Zanza), 3 Wind-Serpent Loas (Hakkar, Quetz'lun and Tharon'ja), 4 Serpent Loas (Dambala, Hethiss ,Sethraliss and Sseratus), 3 Tiger loas (Shirvallah, Kimbul and Xuen), 2 Panther Loas (Ashamane and Bethekk), and 2 black Bear Loas (Ursol and Nalorakk)?