As in fact on the @mamady answer, you can get the name of the function that get fired on mouseDown using getEventListener($0).mousedown[0].listener.name with Chrome dev tools.

As you see, probably the function name does not appears beacause it does not have a named function, so the function is annonymous, but you can see the location of the function:

If it's not, you can see the name of the function:

If the main problem is another (you have to get the name of the function to do something, what something?), please comment here.

Your description is quite different from the title. Do you want the function name that is bound to an event? Or do you want the event itself?

If you want the function name try this in your browser console:

  function asdasd(e) {
    console.log(e)
  }

  let button = document.createElement('button');
  button.addEventListener('mousedown', asdasd);
  let listeners = getEventListeners(button);
  console.log(listeners.mousedown[0].listener.name, "<- NAME OF THE FUNCTION");