Where I work, how we refer to a child often differs on paper to verbally. If a child is known an a diminutive we always use it verbally but only on reports, emails, certifcates etc if it is included on the school system in brackets next to their full name. If there are no brackets then they get called Constance, Frederick, Archibald, Henrietta-Maude etc on paper even if they have only ever been called Connie, Freddie, Archie and Hetty out loud.
Nicknames that bear no relation to the child's name or derive from their surname would never be used by staff - except the Sports dept.
Sometimes children are known by their middle names only. And it's quite common for them to have a British name and a name from their own culture (in those cases the British name is often quite dated or embarrassing and the child quickly prefers their original name - eg Douglas, Deborah, Audrey, Clyde, Eileen, Einstein, Chaos)
There are some very out there/not name like nicknames which I've never been able to bring myself to use, even if the parents do. Usually because I think it makes a beautiful name ugly or odd:
Karizma nn Krig
Muqaddas nn Muck
Phoebe nn Feebs
Hope nn Hopie
Iona nn Uh-oh
Unusual ones I've come across which do get used by teachers:
Joaquin nn Jimmy
Ignacio nn Nacho
Darcey nn Dottie
(all those examples range from 1 - 15 years ago and from ages 2 - 18 for anonymity).