Humans name everything. Sometimes in multiple languages, like the tree in my front yard. It's not simply a Red Maple Tree, it also has a scientific designation Acer rubrum. A good friend of mine named her gun, while another named her car. And depending on which guy you ask, and probably how much alcohol has been consumed, they name their genitalia. Who am I to judge, my naviguesser is named Bessy.
A gun is either a gun or weapon depending on the gun-owner's experiences. But then it can be broken down into more names - 9-milimeter, .357 magnum, etc. Then there is the manufacturer's name. So a gun or weapon is called a Glock G43, 9mm pistol or Brad. The same goes for cars. A car named Jessie could be a truck, sedan, Jeep, or sportscar like a 1966 Mustang GT.
Humans and their names. To be fair though, I don't know any talking non-humans, non-earth bound beings to ask their naming habits and traditions. Every muscle, bone, tendon, ligament, cell, and nerve in the body has a name. Generally two of them. A common name and a Latin name. Ask any med student.
Names are important. They help identify things, places, and most importantly people. New parents probably spend several months choosing just the right name or names for their new bundle of joy. Pet parents also agonize over this decision, but generally take hours or days instead of months to decide. All of a parents hopes and dreams along with identity and heritage is wrapped up in that name.
Naming traditions differ by culture and time period. Today's parents may choose a family name, a more traditional name, or something ranging from slightly different to downright unique. In the last several centuries of the last millennium, European countries used a similar naming pattern for their children:
Early American settlers frequently chose names that were either Biblical (Mary, Joseph, Luke, etc) or were virtues they wanted to their child to possess (Patience, Charity, Prudence). Scandinavians used a patronymic system. Meaning, the son of Eric Olafson is not Lief Olafson, but Lief Ericson (sen is also used instead of son), this is also true for his daughters. This system is still in place in Iceland today, and many Icelanders can trace their ancestors back thirteen generations. From the genealogical point of view -- that one is the easiest to figure out lineage.
Some cultures have a public and a private name, others replace a childhood name with one earned as a step into adulthood, some want unique names, and others want more common names.
Names matter. Naming systems and traditions matter. If you create a culture where all of the male names start with a T or T' (T apostrophe then the rest of the name), you not only should know why -- maybe to honor a leader who passed into legend or a God or Goddess, you should also know why a female is given a name with the T or T' or why a male child does not.
Some things to consider when looking at naming traditions:
How many names does a person have? What is the significance, if any?
If the society is patriarchal in origin, what happens - as in how a child is named -- when a child is born to a single mother? Is there any difference if the child is male or female? What about orphans? And the children of orphans.
What if children carry the name of parent who matches their gender? What happens with transgender kids? or Transgender parents?
Is there a limited bank of names to choose from? If so, why?
Or like was mentioned in Star Trek at one point, are all the names a play off from a God/Goddess/leader's name?
What happens with names at death? Can the name be re-used? Can it be mentioned again? Is it considered a dishonor or a disgrace to not have a child named after an elder, such as a grand parent or elder uncle or aunt?
What about last names? Are they gendered like in Russian names (Alexandrov (male) and Alexandrova (female))?
What happens to names when parties marry? Divorce? Widow/Widower?
What assumptions regarding names are made?
Where I live in the US, the assumption is that when a man and a woman marry, the woman will take her husband's name and all of their offspring will have the man's name. These are practices that are changing, slowly, not only because of same-sex marriage, but because women are choosing to keep their names, husbands are choosing to take their wife's name, or a couple is choosing or creating a brand new name. In my own family - my SIL took my brother's name, my step-sister hyphenated her and her husband's last names, and my step-brother and his wife combined parts of both of their last names to create something completely different.
When building a culture or a world, how someone is named has an effect on their identity. What happens if you have a culture that has a private name reserved for only their closest friends or lovers and their Gods/Goddesses and a public name for everyone else and they fall for someone who has one name for everything? Or a character who in the course of helping a group/tribe/clan out is given a new name by the Shaman. Or chooses one. How those two different cultures and identities play out is another line of detail for a story.
The Importance of Names and Naming Patterns
Surnames in Russia
The Peculiarities of Icelandic Naming
A simple search of 'Naming Traditions' using Google brings up about 85 million hits. Every culture and country has it's own naming traditions and practices. Traditions that have changed over time