Echoing row name where posted ID, for pre-selected form value
<select name="search_category"  id="select1" >
<option value="">By Category</option>
 <?php if (!empty($_POST['search_category'])) { ?>
 <option value="<?php echo $_POST['search_category']; ?>" selected="selected"><?php echo $_POST['search_category']; ?></option>
<?php }?>
  <?php foreach($categoriesListt as $row) : ?>

  <option value="<?php echo $row->id; ?>"><?php echo $row->name; ?></option>

                                      <?php endforeach; ?>
                                </select>

<?php echo $row->name;  WHERE ID = $_POST['search_category']

<?php

    function($id, $table) {

        select ... etc

    }
?>

SELCET('id', 'name' FROM yourTable WHERE 'name' = $_POST['ID'])

<?php foreach($categoriesListt as $row) : ?>
    <option value="<?php echo $row->id; ?>"
          <?php if($row->name == $_POST['search_category']) : ?>
               selected="selected"<?php } ?>>
        <?php echo $row->name; ?>
    </option>
<?php endforeach; ?>