I just did a Google Books search on this word for a serpent biting its own tail and the earliest hit I got was 1884, from La Nouvelle revue, Vol. 26:

But of course this is in French, and I was wondering how far back it goes in English.  The earliest I see in Google Books is from 1899 (Psychism, by Paul Gibier):

It’s not in my old Compact OED; can anyone with access to the online OED tell me if there’s an entry, and if so what the first cite is?

Edit: I just realized it could also be spelled ouroborus (with the Latin -us ending), and that takes us back to 1897:

Finally found it hiding under uroboros. Here’s the earliest cite:

1940 H. G. Baynes Mythol. of Soul vi. 221 Thus the uroborus symbol represents our psychic continuity with the immemorial past.

That 1940 date is rather gobsmacking, since Eddison’s The Worm Ouroboros was published in 1922.  Hard to understand how the OED editors missed that, or why they would decide it didn’t count.

That is indeed gobsmacking.  Thanks for checking!

But the symbol of the snake biting its own tail is extremely ancient. If the name was coined so recently, what was it called before that?

It was probably just called “the snake biting its own tail” (in various languages).  There isn’t a single word for everything.

I found Ouroboros being used in 1922: The Interpretation of Radium and the Structure of the Atom by Frederick Soddy. If you do not confine yourself to English you can find late 19th and early 20th century books in German and Spanish using the variant spelling Uroboros.

Well, as Doc says, the most famous single use of the word was published in that year (that’s where I, and a lot of other people, learned it), and I’ve got an 1897 date for “ouroborus.”

I could kick myself for forgetting Eddison’s novel. It’s one of those seminal works of fantasy which, while you may not have read it (and I never have), the title stays with you once you see it.