I used to put sooooo much stock into naming my characters!! I would look into the meanings behind names and see if I could make some kind of connection between that and who they were or what they were destined for in whatever story I was writing for them. I don't do that so much anymore (still do it for some, I won't lie), but I tend to just go with what feels right or what might fit them best, which might be arbitrary to some! Any approach is valid, and I'm eager to see what some other writers think. Great question!
I usually just try to think of names that no one too close to me has.
I used to spend days on character names and I'd come up with like 12 of these gorgeous unpronouncable names. Now it depends on what kind of character I'm designing. You have to take into account setting too, otherwise you might get a little anachronistic. I spend way more timing naming characters for novels over characters I design for our weekly RPG sessions-- for example, it took days for me to settle on the name Cecily for my latest protagonist, but I made up Presley and Paisley as a pair of sisters almost on the spot for our Pathfinder adventures.
Name generators, sometimes - usually my characters will be called "Character A" and "Character B" until the first draft of the story's done, and then I'll start feeling the whole of the arc out for something that fits.
My MC are always a person I have meet though the years, but I change up the situation of the events. I embellish a fight I witness, and I make it a death scene. Or something that i might have done, and I pump it up. So my MC will be an awesome person and I add different character to support my MC.
Babynames.com! I just thumb through until something feels right.
For me it depends on what I'm writing or where the story is set. Depending on location, the names are a bit more generic or I put a bit more thought into them. But I like to keep a list on my phone of names I really love from people I meet and I use them as needed. Obviously, if you're wanting the meaning behind a character's name to tie into their personality/faults or even their journey to come you have to put a bit more thought in. But you can always change a name if it doesn't seem to work anymore, so I tend to not place a lot of pressure on names in the beginning so long as I'm writing!
I usually give them a stand-in name so as not to slow down the story, and then go back and fill them in later. Nameberry.com is great and easy to use; I also like Behindthename.com, which lets you search based a bunch of factors, including country/language of origin and name meanings!