A Little Improvisation Goes a Long Way
The line “My name is Forrest Gump. People call me Forrest Gump” is one of the most memorable lines in not just the movie, but in movie history. When Forrest uttered these simple words, it was so authentic and endearing, that it became a quotable phrase. But the best part is that line wasn’t even in the original script.

Source: TV Tropes
As he was preparing for his character, Tom Hanks brainstormed and played around with the phrase onset. Director Robert Zemeckis liked the line and allowed Hanks to say it on camera. I think it paid off. Don’t you? It goes to show you that while a script for a film may be incredible on its own, that sometimes the actor can get it even better on a whim.