How to set a value for a span using jQuery

You can do:

$("#submittername").text("testing");

or

$("#submittername").html("testing <b>1 2 3</b>");

You are using jQuery(document).ready(function($) {} means here you are using jQuery instead of $. So to resolve your issue use following code.

jQuery("#submittername").text(submitter_name);

This will resolve your problem.