Naming things is hard work. Kids, pets, places are all examples of this, and characters are no exception. In some cases you can get away with just using a placeholder name until you can find the right name for the character. Nonetheless, when you’re hunting up a name, there are a few things to consider.
The most obvious might be that your character’s name is appropriate to the genre. Although this seems like a no brainer, it is something to consider, especially for genres like historical fiction where you’re constrained by particular time periods. You can’t exactly name your character Yosemite Sam if you’re dealing with Spain in the 12th century without raising a few eyebrows. There are definitely places where bending the rules around names are allowed and thoroughly encouraged (I’d personally say fantasy and sci-fi are the top two examples of this, but please keep in mind I don’t have facts to back that up). Even within those genres however, there are still generally excepted naming conventions and rules that apply.
When looking for a name also keep in mind the meaning of a particular name. We all know Belle means beautiful, and in the case of our favorite Beauty and the Beast Princess, and it suits her well. There’s no need to question what her role is. She’s the beauty, and she’s there to tame the beasty. That being said, also keep the flipside in mind: it’s not all that often that characters get to choose their own names, so a name laden with lots of meaning might also place a lot of expectation on a character. While that can be used to help you flesh out a character’s family life and backstory, depending on how well-known the meaning of that name is, it can also mean your readers bring expectations to the table with them.
In the cases where you need to name characters that are related to another, consider family patterns. Often parents want sibling names to go together nicely (Mary Kate and Ashley Olson; Chris, Liam and Luke Hemsworth; Jaden and Willow Smith; Fred, George and Ginny Weasley; Sokka and Katara). There’s always exceptions of course, but when naming siblings consider choosing a soft rule to go by, such as a specific number of syllables, or that each one contains a certain letter pairing such as double a or an l and an i. Those letters may not need to be together, but they’ll help give a cohesiveness to the group of siblings as a whole. This doesn’t need to be a hard and fast rule though, sometimes names sound nice together without any sort of pattern. And of course, sometimes names within families just don’t match each other.
Also to consider with family names is the generational aspect: sometimes names get reused and varied. A real life example here being that my middle name is Jean and my grandmother’s name is Jeanie. One of my uncles also shares his first name with another family member. That’s all on one side of my family. There are plenty of unique names for certain, but repeating a name from a generation or two ago is an option in some cases.
Finally, when naming character consider the region and heritage you’re working with. Although again, this isn’t a hard and fast rule, many names can be handed down to someone because of a heritage, and most especially with last names as these often are handed straight down from parent to child.