We use a shortening of DD's name. When she was born we told people her full name as we weren't 100% sure what she'd be 'known' as. Over time the nn sort of fit her best so we started using it more; and now most people call her by it. We didn't formalise it. If people asked what we were calling her we just told them both names and let them choose.
FIL calls her a different shortening of her name which is also fine by us.
i think it's best to give both versions. I Know someone who called her baby Edward and really wanted him to be known as Teddy. only, everyone just kept calling him Edward, even though SHE always uses Teddy.
Persoanlly I tend noit to use nicknames unless I am sure it's appropriate- ie, they want other people to use it and it isn't just a family thing.
so def let everyone know that the nickname is available for use