Naming gives life and identity to a person, an object or a place. We personify places with their unique names. Even countries and states have names. Names are an important aspect in world-building.
When a child is born, they are given a name by their parents or primary caregivers. The child reaches a certain age or period and they are then introduced to the larger community, where others acknowledge the child as an unique individual by recognizing their name.
Likewise, when an object - like a weapon - is made, it is also given a name. It takes on a character and personality, becoming real. That is why in fantasy books, you often read about almost-sentient weapons with minds of their own. My personal favorite, the sword, is probably one of the weapons most named by their makers and wielders. I have names for the longswords I use for practice, each with their own particular feel/personality.
Places are named and like humans, they grow to take on distinct characters. Landmarks become landmarks as their names and the unique features that make them special are intertwined. Think of places you love and you will find that they often have special characters and personalities. Perfect, if you are writing that urban/contemporary fantasy.
Given names are the names given by the elder, parents, care-givers or individuals who make/birth/produce/create the children/objects/places. I will focus on human given names as this is something we all resonate with. I will use examples from my diasporic Chinese background.
A child is given their names when they are born. Most parents give names that are meaningful or symbolize something for the child or them. So, if they want the child to be a person of integrity and honesty, they will have a name/characters bearing the same meaning/significance. Some parents will seek advice from their elders or an experienced geomancer who will find names for the child based on the birth date, alignment of stars and planets, and other things.
My own personal name 晓薇 means '"Dawn Rose/Flower", probably because I was born in the morning. My parents thought the name was pretty and feminine.
So, a child's given name is one that gives them their identity, of who they are or - as their parents would hope - the embodiment of the values inherent in the name. The child will grow into the name or be the name.
I hesitate to include nicknames as they straddle between given and found names. Nicknames can be given by loving and well-meaning people in our lives. At the same time, nicknames can be used as insults to poke fun at victims by bullies and cruel people. Some adopt their nicknames in sheer defiance to the people who named them. Their nicknames become sources of strength. Some, however, struggle with their nicknames as these names highlight their weaknesses.
The names given to us might not resonate. We might end up disliking our names (as I did when I was a teenager). Likewise, we might choose to find our own names, the names that truly match our own selves. The advent of the Internet, with various subcultures finding their place in cyberspace, has given rise to online nicknames, many of which that became the recognized names of the users. For people in the New Age and Pagan communities, they discover their true names as they delve into aspects of themselves.
Such names are parts of the whole identity, if not - for some - all of it. Found names are just as powerful as given names. Some found names are earned like deeds. Some are literally found as the person goes through the path of life and self-discovery. And depending on the culture/society you are creating, found names might be as critical as given names in a character's identity.
Let's try this exercise!
Now, depending on what kind of setting you have decided to create, the Fire/Water/Air/Earth chart can serve as an inspiration. They work well in both traditional science fiction and fantasy settings as well as worlds of chrome and steel. Remember to use 5 W 1 H. If you are using - say - fire and water (just playing around with the elements), why are you using them as inspiration for character name(s)? The world can be a hive world, but an individual can still be given (or find) a name that has links to the elements. The trick is to be able to explain why. Perhaps, the individual has ties to a secret group pushing for the return of plants in a world of steel and manufacturing. Or they are named in such a fashion because their parents/caregivers believe in a nature divinity who has survived through the eons like a persistent isotope. Or the individual gives themselves the name as an act of rebellion against the state of their surroundings/environment.