what about Chujung? After the Chinese God of fire. I think that from the description this pet is Chinese inspired, so let's give it a Chinese name! :)
I have two suggestions! I don't know if this was already brought up by some one, so sorry if it was! ;o;
Tasseo - For Tasseography/Tasseomancy or the divination of tea leaves Oneiro - For Oneiromancy for divination of dream immpression
Not sure if they're good enough for an entire species name but I thought I'd try!
Qubahori
-which is quite simple. Quba is made up of Baku, but the Q gives it some unqiue and exotic character; making it extra-special since this is the first pet from Shengui Guo and therefore new and different for users on the site. As for Hori, it's a play with the name 'Iroh'. As I read the description of this new pet, I immediately thought of the Iroh from 'Avatar: The last Airbender', since he loves tea and visited the spirit world as well. Plus, the character of him and the new pet are really alike - gentle and wise. Aside from this, description for this pet sounds quite mature and somehow responsible for me.
Karaodon - would be a nice name
Zentoro - from being a zen totoro
What about Bakuzo? A Baku is a dream-eating creature, while Z? is the Japanese word for elephant.
I vote for this one! This name is perfect. Only change I would make is spelling it as Bakuzou. The Japanese word for elephant ? is spelled ?? in hiragana, which is romanized as "zou", and pronounced "zoh" with emphasis. So it would be pronounced "bah-koo-ZOH".
I also think this one and its explanation are wonderful! I vote for Bakuzou, except maybe to make it Yakuzou
Since we don't have a Y-pet name yet :D
Bakuran?
QELTINAP
= Q + letters from E L E P h A N T + "NAP" (siesta)
Research notes on similar sounding existing words that could possibly be a problem:
Yarrosaur (Yarrow is able to be made into a tea-like drink, which apparently.... according to a google search at least, helps promote restful sleep)

LOVE! Absolutely love these names~
Wanna know more about battling? ❤️ The Official Battle Guide v3.3 ❤️ Need to find books? 🌈 The Book Grind Guide v1.0 🌈
Yrelephin
Everyone has already given some great suggestions. When I first saw the pet, it reminded me of a griffin...not even sure why.
So...Elephant + Griffin = Elephin; added the Yr for something different.
[tot=RiverStarr]
"Valerian" as in "Valeriana" a kind of tea that makes you easy to fall sleep.
"Somniante" a spanish mix between "inSOMNIo" that means "the inability to sleep" and "elefANTE" wich means elephant :D
How about Yume? It's the Japanese romaji for 'Dream' if this new pet is based on a Baku (Sorry if it's been suggested already)
[flower=funkykitsune]
Yerba -- For Yerba Mate, a type of tea from South America.
I've got flames on my chest. It's a lot to live up to.
[tot=Rodimus]
Sayomi -according to the anime web site I visited, Sayomi means "night born".
And if you can stand one more Ganesh name... G'an-tor -a combination of the god, Ganesh, and Tarzan's elephant, Tantor.
If it -IS- inspired by a Baku, Yumekui would be nice if the Subeta version could eat dreams/nightmares. I'm not sure if it is or not, since the Baku is supposed to be a mixture of creatures (Yumenue might be nice, but Nue is generally a specific kind of Japanese yokai -- Subeta is seperated from real world enough where Dream+Chimera could be fine though).
I really prefer Yumetomo (or Yumenue if it's less all-around elephant), as it is dream+friend/companion. I'm sure the artist already has an idea of how they want to incorporate the species into the world of Shengui Guo, but I was inspired by this train of thought;
(On someone asking a resident about the Yumetomo) 'This pet is very popular among residents of Shengui Guo. Originally it was invited into the homes of residents to eat dreams and keep away recurring nightmares - after a while, however, they became semi common in the village and we started taking care of them as pets (feeding and bathing them in an effort to return their kindness).
While they are more active at night, you can find them walking along the streets with their owners, and there are some services that rent their Yumetomo for a night or two in an effort to dispel negative dreams.
Yumetomo are often said to be seen walking through the dreams of their owners, a firm background figure ever-present to fight off nightmares and negative dreams before they take hold.'
Yumetomo isn't really great for a simple pet name, though. Yumekui would work better in that regard.
I vote for Yojimbo.
Because back in the 80s there was was this bizarre rabbit-creature on the ninja turtles cartoons named Usagi Yojimbo that just creeped me the hell out. I can't remember why. I'm not even sure I can remember what it looked like. All I remember is having nightmares over it. And after two and a half decades it's time to overcome at least ONE of my weird hangups.
Please, Subeta. Help me do that.
Besides - I kind of like the way it sounds. It's a name that deserves better than a nightmare inducing bizarre rabbit-creature. :P