yii\base\View has special $params property.

For example it's used for building breadcrumbs in default generated CRUD code templates with Gii.

You can set it like this before rendering:

use Yii;

Yii::$app->view->params['customParam'] = 'customValue';
Inside a controller you can set it like this:

$this->view->params['customParam'] = 'customValue';
Then it will be available in views (including main layout):

/* @var $this yii\web\View */

echo $this->params['customParam'];