I've just had the situation where I needed to setup my Laravel app to update my customer's information in Stripe when they change it in my app.
The method I used to do this is actually undocumented on the official Laravel Cashier documentation, I found it while I was looking through the Cashier code.
In my Settings controller I used the following code to update the customer's name and email when they resubmit the settings form.
$stripeData = array( 'name' => $user->first_name . ' ' . $user->last_name, 'email' => $user->email );
That code should work as long as the User model has the