There's picking names that fit the culture/worldbuilding/etc, but it seems like this question is more about how names fit into the meta, which I come at from two directions
Some stories are more literal for me. I want names that have the right 'vibe', but it's also about finding the name the character would, realistically, be given. Some people choose their names to reflect their self image, but most names are something a parent chooses. It reflects their priorities, sensibilities, and dreams for their child. The difference between a character named 'Chastity' or 'Athena' or 'Meadowlark' or 'Sue' may not or much about the kid, but it tells you a great deal about the parents.
On the other hand, if a story is more silly or symbolic, I might start leaning more into meaning. I really like themed sets. In a comedic story, this often takes the form of filling in side characters on the same pattern, like 'all first names of actors who have played superman' or 'all types of ancient grain'. On the more serious side, it often takes the form of character's names complimenting each other in a way that somehow contrasts, like both being synonyms for different definitions of the same homonym.
I lean towards the first though, and my process usually goes something like:
-What makes sense for them culturally (language, era, class, etc.)
-How did they get their name? What did their namer hope to portray?
-What vibes do I want the name to have?
-Okay now scroll through name lists or throw together sounds until something feels right
