WordPress template page name displayed on screen

If your template file doesn’t have the <?php tag at the top, you should add it.

<?php
/*
Template Name: Exhibition - Pilgrims 
*/

…is how the very top of your template file should look.

Your sample should read like this.

<?php
/* 
Template Name: Exhibition - Pilgrims 
*/
get_header(); ?>
        
        <div class="container fadeIn perimeter">
... [etc]