gravityFormIntToMonthDropdown.php

<?php // Replace the numbered months with named months in a Gravity Forms dropdown date field
add_action( 'wp_footer', function () { ?>

   <script type="text/javascript">
      jQuery(document).ready(function( $ ) {
         $('.gfield_date_dropdown_month select option').each( function(i, option) {
            switch( option.value ) {
               case '1': option.innerHTML = 'January'; break;
               case '2': option.innerHTML = 'February'; break;
               case '3': option.innerHTML = 'March'; break;
               case '4': option.innerHTML = 'April'; break;
               case '5': option.innerHTML = 'May'; break;
               case '6': option.innerHTML = 'June'; break;
               case '7': option.innerHTML = 'July'; break;
               case '8': option.innerHTML = 'August'; break;
               case '9': option.innerHTML = 'September'; break;
               case '10': option.innerHTML = 'October'; break;
               case '11': option.innerHTML = 'November'; break;
               case '12': option.innerHTML = 'December'; break;
            }
         });
      });
   </script>

<?php } );