From everywhere.
I make up random stuff, I use generators, I scour baby name sites/Behind the Name (though that's primarily because I find name etymology/meaning interesting and fun and not because I actually care whether other people "get it", nor do I make it a point to belabor the meaning of a character's name because it's ~symbolic~ etc.; I'm not that pretentious), I abuse mythology, I abuse literature, I abuse video games, I make note of interesting names I hear while listening to conversations on the train or in the store. Sometimes I pick names based on quick word association that may or may not go off into strange places (re: why many of my machop-line pokémon ingame are named "Christian" or similar). Sometimes my characters' names are mostly-random words that are not names at all and probably never should be but I use them anyway—I am dying to find a character to name "Charlatan Break", for example, and please don't ask me why because I don't knooooow. It's just so pretty. ;-;
Right now, for example, I am sprucing up a plot bunny that involves... psychopomps or angels of death, for lack of a better term. In between flails to finish my final projects I've been hitting Wikipedia hard, snagging death-deity-related names for the characters and then bastardizing tweaking them so that they're a bit snappier, easier to pronounce, whatever. Some I just stole directly (Kisin, Neith, Ammit, Samael); some I shortened or twisted around (Muut>Mutt, Ixtab>Ixie, Baron Samedi>Sam Saturday); some I anagrammized or did other strange things to (Malach HaMavet>Heath Malcamav). For more fantasy-related things, on the other hand, I usually make things up or hit Seventh Sanctum. When I make up characters for my fakemon stuff, I usually try to go to BtN and find names that match the type or whatever else I'm doing with the bad name puns (and so at least avoid "Brawly", etc.). Characters whose names I am not etymologically invested in usually come from either my list of "this sounded interesting when I first heard it" or a few button-mashes of the Seventh Sanctum US census data quicknamer. And so on.
Something interesting I've noticed about my own stuff is that I... have a tendency to not like it when character names don't "match", either given name+surname or within related groups. Sometimes I'll get lucky and hit on names that just sound okay without me having to obsess over anything, but other times, especially when I'm going through BtN or whatever looking for names that ~mean something~, I'll find a cool name but then am unable to accept a surname or whatever that doesn't match its language of origin or what have you. My electric-specialist champion, for example, has been named "Voltaire" for a while. When I decided I wanted the league people to have surnames, too, I absolutely couldn't stand anything that wasn't French for him, no matter how nice it might otherwise have sounded. It got to the point where I spent a solid hour or so looking up scientists on Wikipedia, trying to find one that both had something to do with electricity and was French. Then, for no apparent reason, the rest of his immediate family all also ended up with painfully French names. (Including Jacques, which gets bonus points for accidentally also being another bad electricity pun—say it out loud, then go ahead and groan. I'll wait.) And they are not French and there is no logical reason for all of them to have French names. Now my sense of logic is twitching in the corner for the sake of my sense of aesthetics.
And, of course, there's the curious case of a certain probably-abandoned one-shot idea, which has nothing to do with anything Spanish or Hispanic or remotely-real-world-location/culture of any sort and yet somehow magically managed to fill itself up with a cast of Spaniards in a Spanish castle when I wasn't looking. I am still very confused as to how this happened. (And I am probably the only person who manages to get so worked up about this, ugh.)
also protip: if you make up a gibberish/conlang name, or even if you get one from a generator, please please please google it before you get really attached to it. It might already mean something else that other people might even actually have heard of; that something else could be benign but not something you want associated with your thingy, or it could be... not benign at all. I've already had a region share a name with a cricket equipment company, a character whose name was moderately-offensive British English slang, and another one whose name was apparently a threesome sex position. >>; The cricket company one I decided don't care so much about, but the other two changed really really fast. I'm pretty careful about that now, needless to say.
tl;dr awesome names can come from anywhere, for some value of "awesome" that meshes well with whatever the current project is. Or maybe even if it doesn't mesh well but just sounds amazing anyway (Charlataaaaan...)! Even if you have a "pet method" for picking names, you should get into the habit of jotting interesting ones down in a document somewhere, and always keep an eye/ear out for new ideas you might stumble across!
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...can you tell I'm tired and hyper and desperate for simple distractions yet, because I can tell
