It really depends on the context.
Like, when I'm writing, and what the name of a background character, I usually use Wikipedia as a pseudo name generator. Ergo, I get a variety of names from various places in the world. Like, I wouldn't do this if the setting is fantasy, but in a real-world setting, or a setting that takes place in the future of our world and has a clear link to it, I use this method.
If we're talking about main characters, then I'll usually put more thought behind it, and have attempts at deeper meaning. For instance, when I wrote Seven Deadly Sins, I took heavy reference from The Divine Comedy, in that each chapter's epigraph is a quote from the work. The protagonist was named Dante Lodovico - Dante, as a reference to Dante Alighieri (who authored the work), and Lodovico, as a reference to Lodovico Dolce, who wrote the edition that used the name Divina Comedia. Some people picked up on it. Conversely, when I wrote All the World's a Stage (whose epigraphs are all quotes from Shakespeare plays), there's the worlds of Priam and Ithaca, and one of the characters on those worlds is named Troy. It's intended as a double reference, to not only the city of Troy (keeping in with Ithaca and Priam), but also a reference to the idea of the Trojan horse, since Troy is later revealed to be a pseudonym. Conversely, hardly anyone's given a damn about World, and no-one's apparently spotted the link, but that's par for the course (as in lack of feedback).
Of course, this is all fanfic, and I can take reference from the context of the setting as well. For instance, I named the main character of Anthem as "Coda," and you shouldn't have any problems guessing as to why. That said, turns out the world of Anthem is named "Coda" as well, so Bioware obviously hates me. On the other hand, I named Null Sector's leader in Overwatch as "Zero," but that's in the anticipation of him being called that as well, because, y'know...
And if we're talking about player characters with default names, I'll almost always use them - John Shepard, Sara Ryder, etc.
Basically, the TL, DR version is that if you need side characters, use a random name generator. If you're talking about major characters, try and give the names some meaning behind them. That's generally my view, though again, depends what type of setting we're talking about.