Names are important. At least I think so and I fret over them a lot, for both main characters and minor ones. I like a name to be more than just a place-holder. Ideally they should say something about the character they have been bestowed upon. Though there are some names (Adam) that I'll use rarely because they are so burdened with history. And, it has to be said, because they have been so abused in the past.
For some stories, based in particular ages, it's just a matter of consulting census records for the relevant time period and picking a few that seem right. Getting them wrong can wreck a story. I once called a character in a fantasy story Hermes Trismegistus to point up his connection to ancient magics until a reviewer, very kindly, pointed out that it as so outlandish that it over-shadowed the rest of the tale. Everyone else in that story had very down to earth names so it did mark him out too much. Suffice it to say I changed it.
There are many reasons why I can be dissatisfied with the way a story turns out but the most common one is that I didn't quite get the names right. That seems an odd thing to write, but part of what matters about a story is its consistency - in both the philosophical and cookery meanings of that word. Philosophical consistency means all the elements work together to draw a bigger picture. In formal logic, a consistent argument is one in which truth is preserved throughout ie there is no internal contradiction to undermine it.
Cookery consistency means there should be no lumps, the story should flow like a good cake batter with all its ingredients well mixed but still present to the palate when it is served up. Lordy, that was a tortured metaphor.
When I've been stumped in the past, I've tended to go classical and consult Greek and Latin dictionaries for the names of things or traits that I feel a character embodies. Moira means fate! Cool. It's worked pretty well and the intellectual in me likes the etymological playfulness of doing that.
The current work in progress was really stumping me as it is space opera, something I've not written much. With far future SF I was looking for names that are not obviously rooted in the present day but do have a useful meaning. Though I'm aware that's an impossible task. I went classical but nothing I could find really hit the spot. So I tried a different language - Hungarian. Bingo. Almost too many to use. You've got to love a language that has words for black vomit and gelding knife. To my Western ears it sounds sufficiently detached from the present day to be useful yet it has the rigor and rules of a real language. There's consistency in a philosophical sense and it feels good in the mouth. What's not to like.