I was taught basically this same method as the "Princess Bride" plan:
Hello, my name is Inigo Montoya (who I am)
You killed my father (why I'm reaching out)
Prepare to die (my ask / expectation)
Hello, my name is Inigo Montoya (who I am)
You killed my father (why I'm reaching out)
Prepare to die (my ask / expectation)
1. prepare to die (gets their attention)
2. because you killed my father (explanation)
3. I am Inigo Montoya (background info)
Beware of things that "work" in movies. I've been led astray by that too many times.
BTW, ever wonder why movies start out with an action sequence that often has little to do with the rest of the movie? It's to get your attention. Let's face it, you and I watch the first couple minutes of a movie to decide if we want to invest more time in it or click to the next Netflix movie. (Do we care who the director is? Nope.)
Much in life works the same way.
But for other people, one's name is the least important thing, because of course what it most important to them is what affects them.
Once one realizes this principle, you'll see it in action everywhere.
To your point, though, you'd of course tailor this to your audience. For example: you might say "marketing" or "the engineering team" instead of "Tom, Dick and Harry".
If someone is coming to me with a question, it is extremely helpful to know up front who they are (with respect to their role, not so much their name) in order to immediately start narrowing down the relevant contextual parameters that will be framing my understanding of their problem and my response. I don't want to read a wall of text while thinking of how to respond from an engineering perspective, only to discover at the end that the person lacks technical aptitude.