There’s a common misconception when people begin writing that there is a right way and a wrong way to write an omniscient narrator. From concerns I’ve heard I suspect this comes from the idea that at omniscient narrator is an entity detached from the story, although they’re telling it they have no stake in it, so some people assume this means a narrator has to have a detached formal voice. This might also come from the fact that some of the most famous omniscient narrators are from times when people generally spoke and wrote more formally than they do now. By modern standards the narration in Dickens’ book might appear formal but it’s in-line with the standards of his time.
I find the best thing to do, and this might not work for everyone, is to imagine the narrator as a character. This character might not be a part of the story but they’re telling the story to the reader. If we think of the narrator this way then we need to consider this character’s voice as we would with any other narrator. If we return to Dickens’ his style might seem formal by modern standards but his narration is distinctive. Throughout his stories Dickens uses words and phrases that at distinct to a Dickens novel rather than prescribed, he’s famous for his descriptions, particularly of characters.
Another writer with a distinctive omniscient narration is Terry Pratchett whose narration might be considered more relaxed than Dickens and is vivid in its own way with Pratchett’s own particular style of description. If he has a similarity to Dickens it’s that he became known for interestingly described characters. While Dickens and Pratchett both use omniscient narration, and Pratchett has often been compared to Dickens, if you lined them up you could identity they were both by different writers even if you didn’t know who.
Although we may be able to imagine Dickens or Pratchett reading their work to us and omniscient narration is often referred to as an ‘authorial voice’ it doesn’t have to be the author’s voice. It can be any voice telling the story. This doesn’t mean we have to go as far as giving the narrator their own backstory but we could if we wanted to; there have been stories where at the end the narrator has been reveal as a character in the story, sometimes a minor one or one who was asked to write it down. Other times the narrator is a character telling another character a story which is used to book end the story, such as The Princess Bride. Most commonly the narrator has no involvement in the story and doesn’t appear, as a reader we have no idea why this narrator is telling us this story only that they are and this is perfectly acceptable. The general point of a story is that it is being told because something interesting happened and that’s as far as a narrator’s motive needs to go in omniscient narration.
So while we might try to think of the omniscient narrator as a character to help create a distinctive voice it doesn’t mean that we have to form them into a fully rounded character as we would with the rest of the characters. If we want to we can give them a complete story of their own or we don’t have to look at them as a character at all. It all depends on what we find helps us to create a distinctive voice for our narrator.