You can adjust the template to use in the fly based on the type of page you’re viewing. https://codex.wordpress.org/Plugin_API/Filter_Reference/template_include
add_filter( 'template_include', 'portfolio_page_template', 99 );
function portfolio_page_template( $template ) {
if ( is_page( 'portfolio' ) ) {
$new_template = locate_template( array( 'portfolio-page-template.php' ) );
if ( '' != $new_template ) {
return $new_template ;
}
}
return $template;
}
You could use that in conjunction with https://codex.wordpress.org/Function_Reference/get_queried_object to check out information about the page requested, like the title.
This assumes you didn’t just set your page template on the page itself.