It's certainly meaningful, and it runs back into the novel. As I mentioned in a comment on that board, when he's first introduced in the novel he's called "Thomas Hagen." Thereafter in the book and movie he's called "Tom" or "Tom Hagen," never Tommy or Tommaso. And the full name "Tom Hagen" is used in situations where it seems unnecessary, like when he's in the room and everyone there knows him. There's at least one instance where Puzo calls him "Tom Hagen" in three consecutive sentences. My thought is that Puzo, at least, was trying to present as something of a mechanical man, a robot that served Vito but wasn't a fully functioning person.