A panorama is, in its original usage, a wide angle horizontal image. In fact, it's a horizontal image painted in a complete circle around a room. That was in the late 1700s, though, and by the time the idea got to photography, it had been watered down to some degree, generally describing any image with a field of view greater than 100º, and then eventually any really wide image at all. Through that same elasticity of language, it's clearly come to encompass vertical images as well, and continuing in that vein, there's not a clear-cut answer to your question.

On the one hand, "vertorama" is clearly a term people use, and it's pretty easy to understand immediately what's meant. It's hard to argue that it's "not a real term" when there's 12,000 pictures in a Vertorama flickr pool; simply pragmatically, it's a real enough term for that.

But, is it a term with a legacy in photography (or the English language!)? For that, I turned to Google Books search, and couldn't find a single use before 2010. And in 2010, there's this:

Vertical subjects are naturals for vertically oriented panorama (some people now refer to such images as "vertoramas" but we prefer simply "vertical panorama"). – Real World Digital Photography, by Eismann, Duggan, and Grey

That's not particularly a ringing endorsement of the term, and what's more, it's the only book I find indexed that uses it. So, I'd say:

• It's a term people clearly are using and enjoy. It's clearly understandable, and maybe catchy and even clever if you're into that sort of wordplay.
• But it doesn't have a long history or broad acceptance.

If you are the sort of person who enjoys newly-invented portmanteau words, I'd say feel free to use it, but don't be surprised if others view that as a bit ecccentric.