Sometimes people assume that "Julie" is a shortened form of "Julia," but it isn't; "Julie" is my legal name. I never liked when people shortened it to just one syllable--calling me "Jul" (though I guess it's prettier if you figure it sounds like "Jewel")--but my mom does that all the time. (I don't think I ever expressed that I don't really like it. I think I just don't like names that contain long letter U, and the short version emphasizes it.)
My sister grew up as Pattie, but decided in the summer before fifth grade that she wanted to be Patricia, and after some bumps, we learned to call her that. What's funny is now we mostly just call her P. My sister Lindsay gets called L a lot. You probably don't want to know some of the hilarious things Sister L has come up with to call us.
In the first book I wrote when I was fourteen, the protagonist didn't like being called by a shortened form of her name. Her full first name was Cristabel but her brother called her Crissi and she hated it so much that it became a running gag for him to call her that all the time. The next protagonist I had was named Skyler and people called her Sky sometimes but she didn't hate that. My next protagonist was Ivy and nobody really calls her any nicknames except when they're goofily making it longer. She was actually originally named Amanda by her mother (but her mother didn't raise her and her given name was unknown so she got another one later). Her mother doesn't like nicknames and steadfastly refused to call her anything but the full three-syllable name. Her father does the opposite.
Cassandra, protagonist of Finding Mulligan, goes by Cassie. She flirts with the idea of making people call her Cassandra when she goes to college but it never happens. Delia, protagonist of Bad Fairy, doesn't have any nicknames. (You'd better not call her anything cute. And no, it is not short for Cordelia.) She uses a variety of different names later in life, but she doesn't have a problem with her given one. Nick, protagonist of Stupid Questions, never suggests his full name might be Nicholas, and I wonder if maybe it isn't. I have several friends whose full first names sound like they're short for some other common name, so I could imagine someone naming their kid just Nick. (His last name is Harris, and "Nicholas Harris" sounds like too much of the same sound at the end.) And Bay from my unfinished novel Joint Custody has a very good reason for going by "Bay." You would too if your parents named you Bainbridge.
Authors usually handle this pretty well in their books--the fact that people usually have formal names and then names their loved ones call them. If everyone calls a character by a formal name that has a natural shortened form, I always wonder why that is. Changing and shortening each other's names is a symbol of intimacy and familiarity, and I love seeing it in books; it's a nice shortcut to show us history and affection, and also to show lack of it if necessary.
There are always exceptions, of course--like my character Meri Lin who doesn't like to use shortened nicknames for others because she didn't like having a short name and eventually had it legally changed to incorporate more syllables; she was born just Lin. But she calls her partner Fred Fred instead of Frederick because that's what he wants to be called--and even though he loves nicknames, he knows how she feels about her name and calls her Meri Lin as requested. It highlights respect, in the same way my first protagonist's brother repeatedly calling her Crissi highlighted typical sibling rivalry. What characters call each other can tell you so much without saying much of anything.