My character Dorothy is from the 1920s, and I needed a name that sounded old fashioned and was common around that time
There’s a lot of stories, but if you’ll indulge me, I’ll do the main 2 of each of my Big 3 ^^
SANTA FAE
Sherry & Mort, which originally came to me as I was watching my favorite sitcom of all time, Fraiser, who only drank Sherry and Port, and it did strike me as fancy lol. Changed Port to Mort cause of the dead nature, so it worked for me, and then just gave them fuller elvish sounding names out of that 🧝♂️
HEIRS OF DIM MAK
The main character of Reina, a Venezuelan like me, was inspired not by royalty but by my favorite Arepa 🫓 (our signature local food) called la Reina Pepeada (spotted queen) lol. Dim Mak herself is a title, meaning Death Touch in Chinese, and a common phrase for moves that kill instantly, which is what she does as the world’s deadliest assasin and fighter. 
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FRONTIER-0
My very first original story, and the two protagonists, Captain Lily and Astor Roy, were very whimsical. Lily was a name I liked and stuck with, but when I developed the character further, and since she was partly inspired by a Korean friend of mine at the time, she suggested I give her a Korean name as well, which became Eun Nari (used only by her family), which means Silver Flower 
Astor on the other hand was just a pun on Asteroid (Astor Roy) lol 
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For Saylis- c.ai chat that randomly selected a name for me lol
And Matts... well I can't remember because it was 3-4 years ago TvT
My anthro cat protagonist Maor is translated as 毛兒 in Chinese, which means 'fur child', a simple name that is easy to remember & be empathetic to the character. (and also easily translated to other languages)
I have a friend named Callie so I thought about naming my FL Callie, but then for some strange reason I also wanted to name her Texas. So I did both. Her surname is Callaway so her bff/roommate/technically not (in the loosest sense of the word 'technically') not-boyfriend calls her Callie. Her first name is Texas because her parents are a couple of extremely state-riotic Texans.
For my first protagonist, Corrine, she has pink hair, and in super smash bros Ultimate I would often play as pink Corrin.
As for the deuteragonist, I am an idiot because I named her Rose, which also means pink in french even though she has jet black hair. I chose that name because it was meant as a clue to her origin as an outsider. People who live inside caverns would have little reason to name someone after a flower.
My protagonist, Kaito, has his name in Japanese origins due to my very first inspirations being from anime. 
The name's translation roughly means "to soar over the sea", which is a rather abstract meaning when compared to my other characters, whose names tend to reflect their powers, positions, or traits. Since Kaito's power involves being able to freely mimic the powers of others, I decided his name would do well to symbolize some extent of that freedom. There's also deeper foreshadowing regarding the name's meaning, but to say those now would be major spoilers.
2 months later
I usually just use a random name generator until I find one I like xD
Fantasygenerators.com has a LOT of good name generators and I have used it for basically any name I use. Sometimes I'll take a name and adjust it, but since I work a lot with fantasy and I don't need them to have meaning, I just generators.
Oh!!! It's really not a long story - the name just striked my mind so hard that I decided on it to be the name of the protagonaist
For mine, I went with "Iria" because it felt soft but still had this edge to it, which fits her vibe, quiet but not someone you’d want to mess with. I actually stumbled on it while messing around with name generators, then tweaked it a bit. No deep meaning, just that it clicked when I said it out loud.
Sadie Lurker:
For her first name I basically sat their think up names until I thought of one that looked like it fit her. As for the last name the HP Lovecraft story "The Lurking Fear" came to mind almost immediately.
I also thought up in the very beginning that Sadie would prefer the ambush the feral monsters instead of fighting them outright so the last name, Lurker felt right.
Rose Hikari, Rose because it was one of the first things I thought of and Hikari because of Dawn's name in Japan
I almost always use a name generator. I just keep rolling new ones until I get something I like. Then I change a few letters to make it unique. That, or I'll pull names from media I enjoy.
For my current protagonists, 'Vexarok' was a name spat out by a generator that I tweaked. 'Rolec' was lifted from a minor side character in an old video game.
Daecon came about his name in a roundabout way: The first draft of the story I had him called "Hunter", and the story was called "Finding Hunter's Way". For some reason I decided that I didn't like the name, though, and sought a new one. I remembered a tertiary character from the final season of the TV show "Reboot", which was groundbreaking at the time (first CGI animated TV show, mid 1990's). The show was set inside a computer, and the characters were referred to "sprites" (the characters that looked most realistic), "Binomes" (more primitive characters, ones and zeroes), and, of course, viruses (names Megabyte, Hexadecimal, Killabyte, Gigabyte, and, in the last season, Daemon and her lieutenant Daecon). While Daecon played a very small part in the show, only showing up in a few episodes, I've always liked the name, and so I applied it to my character.
I was writing another story and found a character I was writing was more interesting than the protag, who I found more on the bland side. I then rewrote the story around this character, but throughout the multiple changes, they themselves ended being rather bland. I then wrote an Fe3H fanfic, and one of my fav charas to write was Mercedes, so when i got back to Glassflower, I added more Mercedes elements to the character of Setsune
The protagonist of the novel I accidentally started writing, Felix, is named that partially because it means lucky (which he is. It’s kinda his whole thing), but the in-universe reason he was named that was because it was his grandfather’s name (before he got brainwashed into being a secret police and his name was changed to Flower
) which is ironic, because his grandfather has terrible luck. Coincidentally, he has the same name as my little brother 
(It’s a coincidence because I would’ve given him the same name even if my brother didn’t exist) So now I’ve given random slightly relevant characters the names of each of my family members because I think it’s funny. Most of them are in the previously mentioned story, but two are in this other one that I’ll never get around to making but I thought it would be cool if it was an animated musical.
2 months later
At the time I was watching slam dunk, and I really liked this side character, Yohei Mito, who didn't get enough screen time imo, and it happened to have a meaning and ring to it that really suited my character, so I just went with it :]
Lyza - I think the name Lyza is a strong name for a strong female character... when I saw her in a dream, I can't help but to sketch her. She looked fierce and strong and asked some friends like name suggestion and a friend gave out "Lyza, Samantha, Monica...) but Lyza stuck to me... it's a strong name. Not Leeza!!!... it's LYZA (La-i-i-za). It's still very feminine but had an edge to it.
Solaris - Also suggested by a friend... formerly in 2007, when this idea came about, she used to be called "Sarah"... Sarah and Owen. At work in 2011/2012, I was sketching her on my break at work and an English friend, she said "Solaris" and BOOM!!! Solaris and Owen.
Both came friends' suggestions.