How to Display Posts on a Tag Archive Page Based on Custom Field(term meta) Values in WordPress?

Use this-

function custom_tag_archive_query( $query ) {
    if ( is_tag() && $query->is_main_query() && !is_admin() ) {
        $tag = get_queried_object();
        $tag_name = $tag->name;
        $similar_names = get_term_meta( $tag->term_id, 'similar_names', true );

        $similar_names_array = explode( ',', $similar_names );
        $similar_names_array = array_map( 'trim', $similar_names_array );
        $similar_names_array[] = $tag_name; // include the tag name itself in the search terms

        $meta_query = array(
            'relation' => 'OR',
        );

        foreach ( $similar_names_array as $name ) {
            $meta_query[] = array(
                'key'     => 'post_title',
                'value'   => $name,
                'compare' => 'LIKE'
            );
        }

        $query->set( 'meta_query', $meta_query );
    }
}

add_action( 'pre_get_posts', 'custom_tag_archive_query' );

Ensure that the custom field similar_names is set up properly for your tags in the term meta. This code will modify the main query on tag archive pages to include posts whose titles match any word from the similar_names field or the tag name itself.