How do you choose your character names?

Naming characters is so much fun. I especially like giving characters nicknames, because then you can think of a name which tells you something about them or their friends, and then their given name which tells you something about their family background. Here's the thought process I went through for the main characters in my comic Truckstop Demons.
Cal Compson - First name is sort of ironic, since Cal is usually considered a 'country boy' name and the character is anything but. The last name is lifted directly from the family in 'The Sound And The Fury' since the character's home life is similarly dysfunctional.
Lorenz 'Laurie' Furuta - First name is one I stumbled across in a true crime book and just liked, and since the character is half German it fit. Last name is just one of the more common Japanese surnames. I picked his nickname because I think a man going by Laurie is very old-fashioned (like the character in Little Women) and he's a very old-fashioned guy.
Bridget 'Gigi' McClung - I asked a friend of mine from Virginia for a very Appalachian sounding surname, and she gave me McClung, which seemed to fit. Gigi is because I thought it would be funny to have a very butch character with a very frou-frou frou-frou name, and Bridget is the most obvious name for Gigi to be a nickname of.
Cassiopeia 'Snips' Snyder - I started with the nickname. I knew the character was a mechanic, so I wanted to choose a nickname related to that but slightly less obvious. So Snips. Then I thought about what sort of first name would be so awful that you would rather go by Snips. Last name is one of the most common surnames in the region she's from.
I also wrote an entire manuscript for a class where every character's name was pulled from the same mommyblog post of 'the 100 best country baby names'. Laine, Beau, Dusty, Porter, etc. You just gotta find whatever tone is gonna work best for you.

I will be honest... I did not name my main characters... Because I thought at least those names were really important, I had my friend help me. She basically named almost all of them only a select few are names from my head. As for side characters, as was mentioned, behind the name is a great and helpful site for that!

I use things like fantasynamegenerator.com for things like creatures, magical trinkets, secondary characters and other people, but the main characters I like to put a lot more detail into their names by taking names from their background, where they are, age along with other things like that. I always do some looking into the culture of the character for names.

Like my story, The Wizard of Wall Street, the main characters are Kalman Varga, Hungarian and Anthony Lopez, Hispanic. Kalman means reminder and Varga means cobbler because he is from a rather humble background. Anthony means "priceless one" and Lopez is "son of wolves".

I dunno, sometimes something just pops in my head that would fit

I usually get a “vibe” from my characters and then go from there if a name doesn’t automatically pop into my head. I also do the “similar names” trick when I have an idea but not a specific name. Usually, once I settle on a name, the character grows into the name as I continue writing them.

In your case, you might want to try something a little different? What about doing a stream-of-consciousness journal type entry written by your character with his thoughts on names and how he feels about his given name and all his nicknames? Maybe he will come up with his name - especially since it sounds like this is going to be a chosen name, anyway? Just an idea

Post-Apocalyptic Introductions has characters with absolutely crazy names. It makes sense, though, with the explanation that they're names they gave themselves after the apocalypse. I basically just googled their past careers and chose words that were associated with those careers to serve as names. heres what that resulted in:

Agony
Thesis
Duenna
Motif
Sequel

I have a naming system in place for the races in my story, but generally, this is how I go about it.

Humans: (Name) (Town)'(Descriptive)

So Wren Tela'Arwr is Wren because it felt nice, Tela because he's from Telas village, and Arwr which is welsh for Hero. Arya Wilda'Fulmen is Arya because I like the name, Wilda because she grew up in the wilds, and Fulmen because she likes lightning.

Undarians (seafolk): (Name) (Gender)'(Fish-name)

Ghal Ko'Mahi is a male undarian and Mahi Mahi is a type of fish
Syra Ti'Dori is a female undarian and Dori comes from Dory (finding nemo)
I don't have any nonbinary undarians yet but intend to. They use the Ne - modifier

Harpies: (Homeland) (Name)

This one is easier. I have a modifier for the type of environment they were born in, followed by their name. The modifiers are: Ar (mountain), Forest (Er), Uda (ocean), Cyr (swamp), and Olai (plains)

Er Calandra is a harpy from the forest, Ar Neve is a harpy from the mountains. For their names themselves, I go with what feels "right".

I have similar systems for elves and goblins but don't want to overwhelm everyone. As a rule of thumb though, I usually pick a character's actual name based on what feels true to them when I initially write them. I find that letting my characters write themselves starting out tends to yield better personalities overall.

My main character appeared in a dream that I had one night and then decided to sketch her up on paper. This is when I really liked how she looked. Then, I translated her design digitally and thrown it on Facebook and see if many friends could name her.

A friend of mine started to suggest names for my character... some of the names were Lyza, Monika, Daniella and among those names, I did like Lyza. It's a very unique kinda name.

Lyza felt right and ever since, there isn't any other name that match her. So, Lyza it is!

Ask friends if you cannot find names and all.

I stole names from musicians I like. LOL
Gabriel came from Peter Gabriel, and Edwin came from Eddie (Edwin) Jobson.

Random name generator for the win baby!

…But if I’m looking for a specific meaning then I just look up “(girl/boy) names that mean _”

Some I made up haha. My characters Mhehevion (pronounce as May-hee-veeyon), Hiladra, Vilys (pronounce as Fill-lyss), Pravath are such examples.

As my story uses original species, I am constantly searching for what will work for their culture.

Man I hate naming lol I usually pick out a placeholder and end up sticking with it lol Sometimes I change my mind as we get closer. When it comes to character names my only real goal is that the name sounds distinct from other character's names

They call him Shadow

I have a few approaches.

1. Go with a name that hints at their future. Ex. Naming a character something meaning "Guardian" and they end up being someone's(or some planet's) guardian. Or shorten a word to make it a name. Ex. Chara from Undertale is short for Character. Naming a character based on that name's meaning (and how it sounds overall is how I do it mostly).
2. Think of someone you know and name it after them, but use a related name or the same name in a different language. Ex. John can be Jonny, Yona, Joe, Jojo, J, etc. or Sam could be Samuel, Samantha, Samira, Samson, Sammy, Samsung (wait no, copyright)
3. Name it after a song/movie. Ex. I named a character Eileen because of the song Come on, Eileen. Plus I think it's cute.
4. Pick from names you personally like and wouldn't mind attaching it to a character of yours. Ex. I like the name Crystal, so I named a character Crystal.
5. Make it up. If it's a fantasy world, you can go with something completely out there. And it can be from a completely unrelated source. Like in Dragonball, with characters named after food or underwear or musical instruments (looking at you Piccolo).
6. Take the Marvel approach and go with alliterative names. Bruce Banner, J. Jonas Jameson, Peter Parker. If you're that stuck. Pick a random letter and let it take you.

A lot of my characters are from different cultures, so I name them based off the culture they're from. For example, a character in my comic is named Mitali. It is a Sanskrit name because she is from India. So in order to choose her name, I looked up names from where she's from (or based off), and I looked at what each name meant. I chose the name that I fit her in what it meant, and how it sounded. Hope this helps!

1 - Origin of the character
2- Time period
3- Meaning if it's for a important character

If my story was set in a fantasy world i guess i would search inspiration in Latin and Celtic, and play with the symbolism and meaning behind words. ^^

Most of my characters are Korean, so they have Korean names and depending on the Hanja (Chinese characters) that are used, their names can all have different meanings for the same name.

However, I also incorporate a lot of Greek Mythology into my stories to show metaphors and relationships between characters.
Like a Siren is the mythological creature who shipwrecks sailors with their beautiful voices. One of my female characters is named Siren to show that she is so good, one cannot pull away, but also toxic because she leads her partners to their dooms.

Hypnos is the Greek god of sleep, and I use his name for a musician. The musician writes cryptic lyrics as he only sings about stuff he sees in dreams, he's down to earth, and his voice has a whispery, dream-like quality to it.

So, my advice is to turn to Mythology to illustrate who your characters are. Of course, mine are just examples so please don't use them, but any kind of Mythology works for any story, as the gods and goddesses and mythological animals already are a personification of something.
Good luck!