I'm afraid I'm a nitpicker when it comes to details like this. "Ashlee and Pete" didn't give birth. Just Ashlee. :p
The name is... meh. I've been waiting for a celeb to use Bronx. It only makes sense: add Brooklyn Beckham to all the X-boys of the Jolie-Pitt family, you get Bronx. Mowgli is the same as Atreyu, imo. Fictional little-boy heroes.