The public don't need to know who Dan Elwell is, they need to know that the decision to take a very disruptive emergency safety precaution has been taken by the relevant safety body after evaluating the currently-known relevant information. (The people who actually execute the grounding of the Max know who he is anyway)
I don't actually think Trump is doing anything wrong in trying to take responsibility for the action, and suspect the decision was reached through appropriate channels rather than by him reading something by a pilot on Twitter, but having a president known for more being capricious than his understanding of aviation safety as the figurehead behind the decision does make it look less like a reasoned decision to the average person, especially if they have strong anti-Trump priors.