It would work for any tiny
Elizabeth who either couldn't pronounce her own name or had a sibling who couldn't. It's just that once you know that it was the childhood nn of the present queen of England, it's hard to think of anything else.
I was at school with an
Elizabeth, very cultured and elegant, whose childhood nn was Lillet. She didn't know about the, er, feminine hygiene products when she was learning to talk! Nns can be tricky ... :)