I believe that most writers contemplate character names more than they care to admit. They're the one tag we hang on a character that really sticks. The reader might forget that Dirk's eyes are blue, or that Caroline chews the inside corner of her mouth when she is about to say something important; but if the reader forgets whom you mean when you say "Dirk" or "Caroline", we may as well pack up and go home, because the poor reader won't be able to follow the story.
I don't feel that we really invent our characters. Mine sort of manifest, sometimes whole and finished from the outset, sometimes beginning as ghosts and becoming more material as I watch them. The process is more like God, Adam, and the Naming of the Animals: We don't actually create the characters, but we do get to name them as they are paraded before us. It's our little bit. The rest of the time, all we can do is follow them around, scribbing down what they do.
(Nabokov, of course, violently disagreed, stating that all his characters were entirely invented de novo by him with full conscious forethought, and that they were his "galley slaves" who would do whatever he demanded of them. I find this exceedingly unlikely. But, then, I also don't believe that Nabokov truly composed every sentence on its own index card and only later puzzled out how to order these perfect sentences into a perfect narrative. My take is that Vlad liked to test the credibility of interviewers.)
There are certain unstated rules about how we use character names in narrative. In the mouths of other characters, of course, character Jeremy Brooks may be anything from "Jeremy" to "Brooks" to "Jer" to "Snooky-Ookums," but the narrative voice has to settle on something and stay consistent. (Unless, of course, the narrative voice is deeply in rotating POV, in which case Jeremy's naming will change depending on whose POV is invoked.)
True, when you first introduce the the character, you may call him "Jeremy Brooks" in full. If the narrative voice continues to call him "Jeremy Brooks," though, it will have a strong distancing effect on the narrative, keeping us at armslength. (Even more distancing are pseudo-pronoun constructions, where the narrative voice refers to a major character as "the dapper detective" or "the burly prizefighter." Tossing in titles as part of the name, such as "Mrs. Carruthers" or "Professor Smythe" has the same distancing effect, assigning a role and often pushing the character toward caricature or stereotype )
Jumping back and forth, calling our character "Jeremy" at one moment and "Brooks" at another, serves only to make the reader's work more difficult. Do this with very many of your characters and it will seem to the reader that the number of players is multiplying out of control, and three people in a scene can feel like like a throng.
For some reason, using first names in the narrative increases the degree of intimacy and tends to soften the character. Jeremy leaned forward or Jeremy wondered is automatically closer and more kindly disposed than Brooks leaned forward or Brooks wondered. I'm not sure why this should be the case. To some extent it may come from formal manners, where traditionally we must be at a certain level of intimacy with someone before we call them by their first name. But the use of first names also automatically connotes diminutization in the backs of our minds; anyone is allowed, and even expected, to call a child by their first name, even upon first acquaintance.
And this, alas, leads us into linguistic politics, and, even worse, linguistic sexual politics. With Jeremy Brooks, we can choose from the outset that he will be "Jeremy" in the narrative (and, ceteris paribus, closer and more vulnerable) or be "Brooks" (and therefore slightly more distant and also tougher). This is only a nuance, and a thousand things we do in the writing beyond the choice of narrative naming will affect our closeness to, and perception of, Jeremy Brooks; but it is one of our earliest and most permanent choices (and probably says something about how our subconscious feels about the character at the outset). But if the major character in question is, say, "Elaine Carver"...
Well, sorry. She's going to be "Elaine." Refer to her in the narration as "Carver," and you don't just toughen and distance her, you start changing her gender. Reference by surname connotes maleness in our reading and writing conventions--and, for that matter, in most of our conversational style. Women will sometimes refer to other women by surnames, especially in direct address or when the context is chummy, but it's usually kept with a circle of girl-chums. (I had to ponder this problem in Shock and Awe, where Carla Smukowski is, in fact, pretty tough, and, being surrounded by military folk, is often referred to in dialogue as "Smukowski." But she has to be "Carla" in the narrative. [And "Carla" itself is of course a feminization of a masculine name.])
Is this because the language inherently speaks down to women? Is this a way of ensuring that women remain forever girls? Is it tied up with feudalism, where the master of the estate is referred to by the name of his property (his wife being one of those properties)? (This latter aspect lingers on in the fact that, formally speaking, there is such a person as "Michelle Obama," but no such person as "Mrs. Michelle Obama;" she is, properly, "Mrs. Barack Obama.")
I suppose it's a mix of all the above. But if you expect me to take a stand against this convention of our language, don't look for it to happen in my fiction. It's hard enough to keep the tissue of the dream intact without constantly having the reader struggle to keep in mind that the character I keep calling "Carver" is a woman.