How do you come up with character names?

1894 Baltimore Orioles Roster.  It helps to know their nicknames, they become much more colorful.

Print out four alphabets, cut them up into individual letters. Make a circle out of string. Throw the letters into the air. Whatever lands in the circle makes up the name. 

Or just name the PCs/NPCs after my favorite characters from fiction. 

I just go with whatever comes into my head.

Bang on the keyboard a little bit and make a name out of what comes out.

Many of my characters are inspired by characters from literature, which I then completely adapt for D&D into their own character.

My firedancing halfling warlock who sold his soul to escape a wildfire (he begged to the air that he could get away, and the fire stopped and asked "Why?") was inspired by Dustfinger in the Inkheart books, so I named him Dusty.

My half-orc sorlock who I dedicated to being really, really hard to put down was inspired by Kit the Unkillable, from Kings of the Wyld (an amazing book, thoroughly recommend!). I named him Kelgar the Unkillable, to keep the same alliterative style.

My "paladin" (who's actually a celestial warlock, which makes me realise I really like warlocks...) is a joke character inspired by my favourite radio show as a kid, the Goon Show (I'm not that old, but I was given taps by my dad!). The character who inspired him is Eccles, my favourite from the show. Eccles is a lovable idiot, who often forgets that he's supposed to be playing another character in the show. Hence, the character's name is Eccles. Some peak quotes from my Eccles:

When asked which god he serves: "Well, you know when you've been working with someone for a long time, and you still don't know their name, but now it feels awkward to ask? It's a lot like that."

After hiking for 3 hours to a graveyard on top of a mountain: "Did anyone bring shovels?" Eccles: "No, I'll pop back down and get one!"

He (that is to say, I) is/am responsible for starting a tic in the local D&D club, where Eccles will enthusiastically shout "Smoite!" whenever he casts Eldritch Blast. Now, even people who've never met me or Eccles will chirp in with a chorus of "Smoite!" every time someone says "Smite"!

For other characters, it's generally Vibe.

Lugren Hammerhand is an artificer fighter who uses thunder gauntlets and is a pugilist. I picked "Hammerhand" and thought that "Lug" was a good name for a strong bugbear, then lengthened it as he is more sophisticated than most.

Boogy Woo is a bugbear gloomstalker I made for a fairytale game, based on the boogie man and named because I listen to ICP. His whole character is built around being terrifying and just wanting friends.

Talon Blackwind was made as a brother to two characters from a campaign I ran, who were bad guys. Talon is the third of the blackwind brothers (the others were Byron and something else which I forget). I named him because I thought it sounded cool.

Gizmo is my first Artificer, now an NPC. I picked Gizmo, then thought Gizmo Grayling had a good ring to it, then realised Gizmo could be a nickname, so he became Griswold "Gizmo" Grayling. He's a gnome.

Junior is the wild-magic sorcerer autognome which Gizmo built. Full name Griswold Grayling Junior, naming convention inspired by Indiana Jones & the last crusade (Gizmo has a Scottish accent, so it fit with Sean Connery's "Junior!" exclamations).

For PCs, I tend to poke the "random name" button in the character builder until it comes up with something that looks kind of right, and then I tinker until it sounds right.

For NPCs, I either use the tables in Xanathar's, or I come up with a general idea of what names of that culture look like, and that's enough of a framework that I can just make them up.

(Although one of my favorite NPC names is just a straight-up lift from the real world: Thurl Ravenscroft, the necromancer.)

For my current campaign I just cycled through the name generator until I found one that seemed to suit the character. For my “main” however i took descriptive text and made a name out of it. The site I got my idea for my original warlock/sorcerer described it as a “flame weaver.” I had heard of the last name Weaver most recently from Call of Duty: Black Ops, and Flame sounded like it could work in a fantasy setting, so I came up with the name Flame Weaver. I did a similar thing with an eldritch smith and gave him the name Eldritch Smith. I sort of combined the two based on the old famous relative background and got Flame Smith, but he uses his middle name Weaver as his last to avoid attention to his famous father Eldritch Smith.

Op, just asked me to do something i do rather easily then gave me an existential crisis when I failed to articulate to myself let alone anyone else how I do it. 

I think I have several methods or at least principals when doing it, but the simplist answer is "I just do."

Of the methods I use, here are some principals. Where are they from and what would their culture be like? Pick sounds that convey some of that. Some of my Gnoll characters have rough names like Kekechughch, Hreensgul, Gengthris... names that sound like they are made for mouths with different vocal proclivities or have elements that sound like a hyena sound. Hreensgul is like the start of a piercing laugh then a throaty gulp. 

Another principal is to find a trait that character has and then search for a name that means that. The most obvious one in media is naming a combat leader that guides people through a crisis 'Shepherd.' There are so many IPs with a Shepherd as a main character that it is easier to just say have a look then list them.
You can also do the opposiste of this technique and give someone sweet a really dire name. Had an Orc cleric named Gogeskront Throatbreaker who was very gentle and went by the nickname "Runt." 

You can also look at mythological names and either pick them or derivations of them. You can also go for cheap gag of giving your character the same first name of a figure from the world but then not liking to be mistaken for them.  "No, I am not that Bruenor!" 

I have tons more but I don't feel like seperating them from my subconcious then writting them down.

Sometimes you can just let your mind go blank and stare at a doodle or description of the character and see what pops into your head. 

Well, obviously I light candles, throw the rune sticks, call on the old gods and then make the required food offerings on the stone altar in my hidden shrine following which, I ignore all of that and go with some version of a middle or old English or old Norse name.  Season to taste.

Ah... looks at the date of the OP. But the topic is worth it. So here are my methods over the years. 

1st character name given by DM, as the character sheet was a handout. This was during the age of it's D&D or AD&D. Will not elaberate. 

Names from the Past I did make, and how. 

Gilbert Alfhiem. - Pscionist Elf. AD&D, Gilbert was one of the two protaganists in RotN.  Alfhiem means Elf Home. 

(Redacted due to me being dense) - using a thing in the world I like and reversing the spelling to make it sound alien and cool. My Elf War-wizard AD&D valley elf (Grey Hawk)  was named for a soda I was drinking as I rolled her stats.  Had a hyphan and everything looked really cool, and I kept saying her name without noticing what I was saying for a year. Didn't realize it until the campaign ended. Yeah, will never forget how bad that was. - really worth a D&D horror story IMO, but I can not say the name. 

Mariel, MaryHell, Marielle, Mary Hell.... my name or what would become a part of my name IRL as I was unconsciously figureing out my name as a trans woman, without being self aware of it. 

Sucram .... male character Marcus backwards, I took names I knew and reversed them. Llednar, Sucram, Trebor, Nivek, basically any male character would get a name like this. 

Bhuemkabhuem (Avatar Rock Gnome) - how to spell a common thing or word wierdly. Boom Ka Boom. Also Dhuembhuenay for a cleric. 

Bhump... my tobaxi ... random keyboard press with eyes closed. 

Gail Alfhiem. You know that nerd character I made, well he died by geting teleported to the negative energy plane. Never sat well with me. So I made that character again, reborn by the will of a goddess into the Shadowfell, as an elf maiden a Shardar-kai now, who was a Death Cleric of (That goddess) 

And finally based on a book series I was reading Shaye she is my trans Tiefling Warlock. Basically took a character name and made it femme.