I've been called Toria for years, and am in the process of officially changing my name from Victoria to Toria. I like the shortening of it, because Victoria is too posh and Vikki is too common. Toria is just right!
This certainly beats Vicki and variants, and it sounds less like the horrible British and Canadian conservative parties than Tori. It still does, though, which is why I won't warm up to it.