Elyzabeth

This name is listed as a rare variant of Elisabeth/Elizabeth. It isn't a rare variant, it is a misspelling, invented by someone who wanted to be different. It has no history of use. (I'm aware that it has been bestowed a few times on unfortunate children who then have to spend the rest of their lives spelling it out and repeating that, yes, that really is supposed to say Elizabeth).

No, it's not a misspelling of the name. I think it's archaic, rather. Elizabeth of York's signature reads "Elyzabeth the Quene".