Using search.php without a ‘s’ field in searchform.php

I am not sure as how to get around using id="s" in the input field. But just to clarify, I believe wordpress is doing something like $input = $_POST["s"]; when the search is submitted. The id="s” is necessary because it tells the php script from which html input field to pull the input from. WordPress would then do all kinds of stuff to the $input variable and search the site for it. Not a solution, but hopefully resolves some confusion.