As for people shouting the character's name at him, it's unlikely that happens on a regular basis. While the film is popular, it's not a massive cultural phenomenon like some of Damon's other films. However, it's possible that some fans might recognize him from the film and make a joke about it.
It's important to remember that Matt Damon is a very successful actor, and his career is built on many other projects besides "Team America." While the film is certainly memorable, it's not something that defines his entire persona.