But PuppyMonkey if your birth certificate says Betsy (or any other diminutive) then you can't lengthen it, as for anything formal your name will be Betsy, unless you change it by deed poll. People will therefore call you Betsy, and look at you very oddly if you then say "it's Elizabeth actually". Whereas the other way around no one blinks an eyelid (is that the right expression?) indeed, people often will ask what you like to be known as when you introduce yourself by a formal name (which personally I find irritating, but there we go).
Personally I have always been know by my diminutive by family and my formal name by everyone else. I would have hated not to have the option.