Well, I haven't seen it, but I do know that there is a Quebecois remake of a French play-turned-movie that was part of the Just for Laughs comedy festival. In the story, the guy (Vincent) is going to be a father for the first time and he goes to his sister's place to celebrate. When he reveals the name that he intends to use, it sends everyone into a tizzy (as you can imagine), and during the movie, as they wait for the pregnant spouse (girlfriend?) to arrive, the name issue is basically a catalyst for exploring their views, beliefs, and deep dark secrets. It's supposed to be quite good, from what I hear. Sorry I can't provide personal experience with it.

One of my memories from my childhood was from a comedy called Trying Times. Teri Garr's character was talking about the name she was planning to give her son. She said, no, she didn't want to talk about names beforehand, because well, there are always people who'll say something like that was the name of a plumber that did a shoddy job, that was a horrible ex, that sort of thing, and ruin the moment... Okay, they're naming their son Adolf, so that he doesn't feel like he has to live up to anyone's expectations.

I've seen the trailer and I'm absolutely going to watch the film as soon as it's released in my country. 

Are you familiar with French films? They have their very own and very unique comedy genre, and I can't think of a similar American film that fits this genre. I suspect from what I've seen and read about Le Prénom that the name is more like a catalyst for all the hilarious drama than a central theme in the film.