Shadow Names are the names Mages use among themselves.
When a newly awakened Mage enters the complex society of orders and consilia, he is strongly advised to use a so called Shadow Name. Names -True Names in particular- have power, because they are a connection to the entity they denote. An enemy that can't be accurately named is an enemy that can't be easily targeted with magic. A mage uses his shadow name the same way an attendee of a masquerade ball uses a mask. Not only does it hide his true self, it also facilitates the mage's taking on a different persona, ideally one that is better suited for working magic.
Shadow Names can be anything that fits for the mage. Myths and religions are common sources, as well as history, philosophy and anything else that the mage associates with himself.