Identity in The Martian Chronicles is not just a question of masks and playacting, although it's that too. (Stendahl uses robot lookalikes to trick everyone at the party, even though it would seriously be easier just to shoot them all.) It's mostly important, however, because we've got two cultures meeting, trying to communicate, and figuring just what the other is all about. One of the first things they have to communicate is who they are. Think, for instance, of Tomás Gomez and Muhe Ca in "Night Meeting," trading their identities before going on to form a strange sort of friendship.
In The Martian Chronicles, masks—whether literal or figurative—can't hide true identity. All the characters in this book eventually reveal their true natures.
Identity in The Martian Chronicles relies on names. Identity is a social construction—you are what others say you are.