What's in a Name?
I do some editing for other writers, and one of them, a beginner, asked me for advice on how to refer to characters in his book. First/given name? Family/surname? Both?
The answer is, as with so many aspects of this craft, "It depends."
I'll go through the options, but first there is a distinction that needs to be made between narration and dialogue. Narration is anything said by the narrator. Easy enough. Dialogue is anything said by a character. When I discuss each option below, I will distinguish between these two settings.
In narration, (usually) use both names when first introducing the character. This helps the reader understand which names refer to that character, even if a different one is used in some dialogue. After that initial introduction, use the first name only if the character is a child, or if the tone you're going for in the book is very personal. Crime and thrillers use last names almost exclusively, as do action and adventure books. Fantasy can go either way. Romance often uses first names, children's and young readers' books often use first names in narration.
The first name can be used in dialogue in any situation that it seems natural for the speaker.
A parent speaking to a child would use the first name or a nickname (or pet-name). If the parent is angry, the child's full name - including a middle name - might be used. The narration surrounding this dialogue would be consistent though. Whatever choice you make for your dialogue should not vary without a strong technical reason or purpose.
If a character speaks to a world leader or royal personage, use the proper title, unless the relationship is personal enough to use the first name. So if a character meets an important person that she doesn't know, use the title and the name. If it's a princess talking to her sister the queen, in a non-formal environment, then first name usage is appropriate.
Feel free to break these rules though, if it's for a purpose. An unruly mountain man might meet a princess or a queen and call her "missy," or by her first name, and though it's socially inappropriate from the princess or queen's point of view (and probably the readers'), it may be appropriate for the mountain man, or you may be highlighting the lack of respect the character has for convention and formality.
Remember, it's only breaking the rules if it's an accident. If it's a purposeful choice, then have at it.
As mentioned above, genre norms will often dictate the way the narrator refers to the characters. This assumes that the narrator is anonymous. If the narrator is the character's parent, spouse, child, or something similar, then really the dialogue rules apply. In normal cases though, consider the following.
Using the family name makes the character seem tougher and less personal. Think "Reacher" "Rambo" or "Holmes."
Using the first name softens them, think "Peter" (Hook calls him Pan) "Anna" (The King and I) or "Annie" (the orphan).
The problem and complexity comes, of course, when you have different needs for different characters. What do you do when you want your main character (a leading man for example) to be tough, but your secondary character (leading lady) to be soft and personal?
One technique I suggest is to give the lading lady a softer family name. A flower, a beautiful Italian name, something French and flowing... you get the idea.
I don't recommend mixing them - using the family name for the male and the first name for the female. Not only does this seem inconsistent, but it risks coming across as misogynistic. The reader will probably sense it, but may not identify what's wrong. The effect will be a sense that the story itself, or the writing as a whole is off. Unless you're going for a sense of dissonance, keep it consistent. As a rule of thumb, follow the norms of the genre.
Almost always use first names for child characters.
If more than one character shares a family name (brothers, spouses, a sprawling family) then first names are necessary.
If you have a reason for breaking with the norms. For example, "Madonna" is the singer's first name (Madonna Louise Veronica Chiccone), but we would never refer to her as Chiccone in a story's narration, without a solid purpose for doing so. Dialogue, however, would likely do so often.
I know I haven't covered it all here. There are dozens of other circumstances that will complicate things and cause you problems when you're writing. Don't worry about them. Err on the side of genre and consistency. If you can articulate the reason to break the rules, then go for it.