Only
Beth I've known was a whiney brat, often called Bethy! I've never met a
Beth that was short for
Bethany, though I've heard of it happening - one reason why I prefer Betsan to
Bethan (I don't go for
Bethany at all).
I'd use
Elizabeth and let the nn take care of itself.
Beth as a name in its own right would elicit the same question eleven times a day for all eternity.