This one should seem pretty obvious:
Character names matter. And they matter the same way that accurate details matter in a piece of writing. They add a level of meaning and depth and interest that otherwise wouldn't be there.
I also argue that it matters more for side characters. Sure, you can have a bartender named Bob. Bob is a good solid name. I have many friends who are named Bob. But is 'Bob' saying what you need the name to say?
So let's imagine that you have a bartender named Bob in your story. He comes in, let's say, two scenes. He gives a key piece of advice to the main character. Not a life-changing event now, he's just making the Main Character think. I imagine that Bob, being a good solid name, would give good solid advice. If that's what you want as a writer, great! Mission accomplished.
Now name the bartender Lacey (he's still a he).
Now name the bartender Chad.
Now name the bartender Alexander Who Calls Himself Great.
Now name the bartender Adolph.
Now name the bartender Michelle (she's a girl).
What happens to the flavor of the piece? Even if they all give the same solid Bob advice, there's another layer at play. Do you listen to surfer Chad the same way you listen to some whacko calling himself Alexander the Great?
A fun exercise is to go into a smaller scene in a novel, and switch around the side characters' names. Or even name a character that wasn't named before. See what happens. See if there's a layer that can be added, what depths there are to be explored.