I'm most stories, the character name should be chosen very carefully. Look at some on the great stories, and you'll see that the character name can help advance the stor or give a memorable performance the extra it needs.
For example, in the movie "Fire Down Below," Steven Seagal plays a character nammmed Taggert. In Scotland, it translate to "on of a priest."
In this movie, he starts his investigation working for the local church. And as the story progresses, you find that he cannot be corrupted, like he was really the son of a priest.
When i write my plays, the character's name always has a root into his character. Here is an article that appeared in Writer's Digest "The 7 Rules of Picking Names for Fictional Characters"
In the introduction paragraph, it explains in a nutshell the importance of picking a name before going into the seven reasons:
Choosing a character name for your novel is as pressure-filled as
picking a name for a baby. It has to suit the character’s personality,
makes sense for the era and, most important, be super awesome (sorry
friends, the awesome name of Brian A. Klems is already taken by this
guy). Names like Harry Potter, Holden Caulfield and Stephanie Plum are
memorable not just because of the amazing stories they navigate, but
also because these names “fit” those characters so well. You need a
name that “fits” your character too.
Care in your character names is just as important as your story's plot. For many may forget what most of the plot was about, they surely will remember that memorable character, so long as his or her name fits the story like a glove.