I think it really just depends on the script. In some cases, a name that "means" something can give you a sense of the character themselves, taking into account the etymology of the name itself. But, unless you go out of your way to explain the origin of the name, it may just be a "name" to your audience.
It depends on the character. For instance, for a short script I wrote at KU, the story was about this girl who gets tired of having to park forever and a day away from her dormitory. So she starts going from one dorm room to another trying to get a petition signed so she can have her own parking space right out front. She meets a couple of stoners who think that this is just cool and, of course, as they tell the story of this girl to their friends and as they pass it on and as THEY pass it on, her "legend" becomes just HUGE in its own right until, at the very end, when she goes to the administration building to turn in her petition, the entire 20,000 population student body stands outside to back her up in her quest for a private and reserved parking spot. The whole thing ends with a giant mob sequence of the students running down Jayhawk Boulevard toward the administrators. Now, all of this is a roundabout way of coming up with her character name, Nike.
The reason I chose the name Nike was because it's an uncommon name, a well-known word, but it's the name of the Greek goddess of victory. I could have named her Sarah or Jessica, but I thought an uncommon name worked well given the story.
On the other hand, I have tons of scripts where I just come up with a name which has a sound I like. They can be common, like Jason or William. And they can be uncommon (although they don't actually "mean" anything) like Arri or Jasper -- both of which I have used.
The trick is don't use a name just because it has a backstory or some kind of history that you like, unless you are going to explain that as part of the character development. For instance, if you name your character William because he has a personality like William the Conquerer, the audience would never know that unless you wrote a scene where he explains why he was named a certain way.
Other filmmakers have gotten around the question of names by using different monikers for their characters. Clint Eastwood was notorious for playing the Man Without A Name, who goes through the whole movie without ever revealing his name to the audience. And then there is Quentin Tarantino. In Reservoir Dogs, he gave each of his characters a nick name and made a big scene out of it (the Mr. Pink sounds a little too close to Mr. P***y speech). Then, in Kill Bill, the Bride commonly talked to her co-horts using their christian names, but he beeped them out.
There are all sorts of creative uses for names. It's just a matter of deciding when a name is important for character development, and when a name is just a name.
