Jeff, I had a friend in fifth grade whose mother decided he should change his name because she was getting remarried. He was old enough to choose (and I think even 4 is old enough to have some say in this matter!) but she didn't ask him; she TOLD him this was going to happen. He wasn't the type to rebel, and he was nervous of if not actually afraid of his stepdad, but he was NOT happy about this. He felt that it was one more thing distancing him from his dad, that his mom was trying to pretend she had never been with his dad. Also, his original last name was just a nicer name and sounded better with his first name.
I also knew several kids who, at various ages between kindergarten and high school, were adopted by their stepdads and therefore given stepdad's last name. All of the biological dads were completely out of the picture. However, in every case, the kids were irritated by the name change, because they saw the original last name as their OWN name and resented having their identity switched midstream.
I can understand your ex feeling it would be more convenient if everyone in their household had the same last name. However, there are other factors to take into consideration. She might be concerned about "what people will think," but these days there are more and more families with various name configurations, so I doubt your son will encounter any problems in school, etc., if his last name is different from his mom's.
I think it is a particularly bad idea to have your son use a different name than is on his legal records. This will cause endless confusion whenever he does anything involving paperwork: enrolling in school, getting a bank account, getting a job.... Should he ever have any run-ins with the police, having an "alias" will make him automatically suspicious to them even if he's totally innocent.
What if your ex's new marriage doesn't last? Will she want to change the poor kid's name AGAIN?!
Do you and your ex get along well enough that you could sit down together with your son and talk with him about what it would mean to change his name and see what he thinks of it?