From Maragaret -> Marguerite (French equivalent) -> Oxeye Daisy (Leucanthemum vulgare, named Marguerite in French). So it's a bilingual pun.

Elizabeth -> Judy follows a very different route, being one of those idiosyncratic examples which confounds any normal logic. My mother is named Elizabeth, but when she was a child, she gained the alternative moniker Jude after St Jude, the patron saint of lost causes. This name is one used only by her two (much older and now deceased) brothers and their subsequent families, so I would never hear it unless visiting the cousins.