Wrap contents of the Event Espresso Thank You page with a div, and include a category class name if there's a category set on the event.

thank-you-category-div.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

add_action( 'AHEE__thank_you_page_overview_template__top', 'my_custom_div_class_thank_you_page' );
function my_custom_div_class_thank_you_page( $transaction ) {
    if ( $transaction instanceof EE_Transaction ) {
        foreach ( $transaction->registrations() as $registration ) {
            if ( $registration instanceof EE_Registration ) {
                $event = $registration->event();
                if ( $event instanceof EE_Event ) {
                    $events[ $event->ID() ] = $event;
                    $category = $event->first_event_category();
                    if ( $category instanceof EE_Term ) {
                        $category_slug = $category->slug();
                        echo '<div class="' . $category_slug . '">';
                    } else {
                        echo '<div class="no-category">';
                    }
                }
            }
        }   
    }
}

add_action( 'AHEE__thank_you_page_overview_template__bottom', 'my_closing_div_thank_you_content' ); 
function my_closing_div_thank_you_content( $transaction ) {
    if ( $transaction instanceof EE_Transaction ) {
        foreach ( $transaction->registrations() as $registration ) {
            if ( $registration instanceof EE_Registration ) {
                $event = $registration->event();
                if ( $event instanceof EE_Event ) {
                    echo '</div><!-- end category -->';
                }
            }
        }   
    }
}