I kinda...just go with it? Like while I'm writing, I just put down the first name that comes to my head then change it later. One time, my big, bad villain was named Timmy.
I name my characters after drawing them and after I at least have rough storylines planned.
Regarding how I give names, I really like two-syllable names! Idk why lmao. Also, I have this weird belief that since my drawing style is very manga-like, it's weird for my characters to have English names (lmao). But I also don't want them to have Japanese/Chinese/Korean names since I'm not from those countries. And so, I usually choose names that don't sound completely English/Japanese. Something like: Rina, Noa, Mia, Lia, Karen, Lana, Rena, Mana, Sian (yes, all female names).
I also like English names from different origins:
Tomas (instead of Thomas)
Iren (instead of Irene)
Klara (instead of Clara)
Etc...
If I'm stuck, I usually google baby names XD
Also, if I meet someone/see a name that I like, I tell myself "that's going to be my next character's name" haha.
I name my characters as I write, and I guess that's a bad thing since I write many stories at the same time. People have pointed out I have 2 Wyatts, 3 Christophers, 2 Olivers and 2 Ethans (They're all from different stories.)
Oh well, I'm not one to go for basic names, nothing too extraordinary or out there.
I usually just skim through a baby name site/name gen until I find something that clicks, then I build my characters around that.
It really depends on the story and what kind of mood I want! If Im writing something spooky, I'll name it right away. Fantasy is an iff because I have to search for a name. Or sometimes, my characters have no names because they've been lost through time within their story and is referred by a title.
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i give them bad placeholder names until i get better ones and then end up getting attached to the placeholders
alternatively, as with my character jack: forget his name was supposed to be jake and get attached to the Bad Memory Replacement
Much of the time I'll do research. In recent years Behind the Name has been my go to site.
Other times I'll just use whatever name pops up in my head.
But they always have to fit the character that I've already drawn out/envisioned in my head. I don't think I've ever had a name first and created a character around that.
I'm with @Ringarune here - same with me =P
I first create the character, what's he/shes personality? Looks? Life/Past? Then I give them names. I useally do go to http://www.behindthename.com/1
from there I choose the names orgins, how it match with the character. Whats the names orgin?
If I dont find any I like then I combine two diffrent names and make it sound right. That fits more with Fantasy-names
I just kind of choose names that sound good. One of my characters has a name that actually means something and the rest are chosen just for kicks.
(Actually for one of my characters I asked my jazz teacher to say a random last name and assigned that to him lol)
Most of my stories take place in an alternate earth - very similar to our own.
Therefore the name choosing consists of searching nice sounding names in different languages, depending on the characters background and ethnicity. I also lookup the meaning behind the names - coz y not 
Examples :
Salvatore Marchesi (italian dude)
Jinan GÖKÇE (turkish girl) - goes by Jinny
Eutychia Kosmidi (greek girl) - goes by Efi (pronounced Ehfee)
For me its not what i like, its what i want to tell the reader. The name should be apart of the story, not just something i like.
I grabbed letters, and put them together... this did not always have the right effect..
once i had a character names: Porgasius....
-Google names and then look at what they mean
-Name that I like and look up similar names
I try to look for names that are easy to say/ sound nice and suit the character personality
It depends on the characters importance for me, so if it's a main character or one who's got a big part usually design and personality elements come first then find a name that fits. Some cases a character goes without a name until some of the story or background about the particular characters been written. Other times I'll just pull a random name out of a hat and that's it.
There's also throwing an arrow blindly at a dartboard but only if naming has gotten boring, or it's become too difficult, does that option come up =w=)
I do that too, I give them titles based on the things they do. What I do is imagining myself as a random bystander or a person witnessing them for the first time, whatever pops up in my head will be their nickname.
Like a girl who can transform into a powerful magician that mainly harnesses the power of fire, along with her transformation her black hair turns red and her brown eyes, crimson. My first impressions were "Crimson mage" or "Infernal Flower" But then I remembered that this particular character was a maid. So it hit me, "Blaze Maiden"
I'd give them names afterwards, but I focus more on their personality and backstory first. After I've finalized that, I'd poke google to give me a list of suitable names for them.
Depends on which story and what they need to be.
If it's a just on Earth or if it works, stuff like Steve.
If it's in a fantasy setting, I usually just type gibberish or break out google translate and find the most exotic words.
I gotta have names early on. I don't feel right referring to characters as "the tall blonde one" or some such. I also feel like having names helps me with character development. It's much harder to name a character that's fully fleshed out, rather than a fresh new character. I really struggle with names anyway though, so I always tell myself the early mediocre/terrible name are placeholders. But 9 times out of 10, I get so used to using those names, that I never really change them. If I try to change them, I end up constantly switching back to the old name on accident.
If I'm determined to have a great name for a character, I'll ask my partner, and he'll let me borrow a super cool unique name from his pool of potential character names. Feels bad stealing a name from him though lol.