To change the name on your subscription, sing into your WeeBox account here and click on my subscriptions. You will then be able to edit your delivery details by clicking on 'Edit Delivery Address' and entering the correct details. This will change the name your future WeeBoxes are delivered to.
If you need to change your billing information, click 'Edit Billing Information' in your subscription details instead.
If you need to change the name on your account, you can find out how to do this here.