How to tell Siri <<EOF>> when I am done talking, eg, over steady background noise?

Solution 1:

If you press and hold the Home button down and keep it down the whole time you are asking Siri the question, letting go of the Home button will signify "end of question." It takes a little getting used to but it works great. This is not exactly what you asked for but it solves your problem.

Solution 2:

There is no way to give Siri an EOF-type word that you're done talking. Similar to what @dennismuys said in the comment, you can tap the Siri waveform on the screen when you're done talking.

While this isn't the key-word you're looking for, it will serve the same purpose.