I really don't think it can be called a classic in the same way as
Elizabeth or
Mary can. To be a classic I think the name has to have enjoyed fairly steady use right along, and
Tiffany hasn't. It may be classical, but not classic. And I would advise anybody who wants to use the name
Tiffany not to try and tell people how classical it is, because it won't ring true even though it is.
If I was reading the birth announcements and saw a
Tiffany, I'd smile. It's a pretty name, and it would be a welcome change from all the Kaylees and Emmas and Sophies and Addisons.