Enter a variable in the ‘category_name’ parameter

Yes you can pass the variable in category_name. But I think it should be get_the_title() instead of the_title().

$title = get_the_title();

$args = array(
    'category_name' => $title
);

Try this. But remember category_name only accepts category slug, not category name.

You can also use following method if your page title/slug are different. And I think it’s better.

if ( is_page( 'Page Name One' ) ) {

    $cat_title="red"; // should be category slug

} elseif ( is_page( 'Page Name Two' ) ) {

    $cat_title="yellow"; // should be category slug

} elseif ( is_page( 'Page Name Three' ) ) {

    $cat_title="blue"; // should be category slug

}

$args = array(
    'category_name' => $cat_title
);