Jiyishu

Jiyi + Yishu (Memory + Art)

Zoji

Zo + Ji(yi) (Elephant + Memory, kinda)

I like Leophance or Liophance

Qeffalum. KEF-faa-luhm.

It's basically just 'heffalump' with a 'q' in front and no 'p' XD

Tass.

Chanfa

Quindao

Also, I don't know, I kind of like Phanty McPhantface.

Chanok - the korean word for green tea (nokcha/nogcha) with the syllables switched Qanok - same thing, with a q

Tulsi is a Hindu goddess that was the called the "Queen of herbs" and it is pretty close to the work "tusk." Plus it's pretty cute. Tulasi or Thulasi are alternative ways to spell it too I believe

Bakushan (Since Baku are dream eaters in mythology) Leusa

Bakucha Baku being the japanese dream eater, cha for the chinese term for tea.

I am very creative. Haha.....ha....

My suggestion for the pet species name is Rajan. (From Gajraj - "elephant")

Other suggestions are Vinaka and Ghanati, the latter after "Ganapati", an alternate name for the Hindu elephant deity, Ganesha.

I like Elephabat or Woolaith

Qureshi (common Muslim family name; just like the way it sounds!) Yasumu (in Japanese, yasu means 'peace, quiet, peaceful', mu means 'dream, vision') Zhilan (in Chinese, zhi can mean 'wise, intellect' and lán can mean 'mountain mist') Utembo (since we're lacking an U-named pets, and tembo means 'elephant' in Swahili)

Maekti - maek is the korean word for baku/tapir, ti sounds like tea, the whole thing sounds like "make tea". this one is a little cheesy.

Mengxiang

Bakkuya

Mammathee

Ganaphant

Bindibakku

....I'll think of more later

Hoshui ("Hoshi" + "Shuìjiào")
Seoshi ("Seishin" + "Hoshi")
Yinaku ("Yin" + "Baku")
Quorai ("Quo" + "Raion")
Kuoshu ("Kuma" + "Shuìjiào")

Primordial

Yuan-esh(a) - A combination of Yuan-Ti and Ganesha.

Phanorioum, yep definitley

Naheisa